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rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) simple abelian varieties of prime dimension; Hodge conjecture on algebraic cycles; zeta-function of the abelian variety; Tate conjecture; Mumford-Tate group; Mumford-Tate conjecture DOI: 10.1070/IM1983v020n01ABEH001345 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Calabi-Yau 3-fold; topological string partition function; Gopakumar-Vafa invariants; BPS states; D-branes; Taub-NUT geometry; wall crossing; free field Fock space; M-theory compactified down Aganagic, M., Ooguri, H., Vafa, C., Yamazaki, M.: Wall Crossing and M-theory. Publ. Res. Inst. Math. Sci. Kyoto \textbf{47}, 569 (2011). arXiv:0908.1194 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves over global fields; Mordell-Weil group Shoichi Kihara, On an infinite family of elliptic curves with rank \ge 14 over \?, Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), no. 2, 32. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cohomological theory; group of cycles modulo rational equivalence; Chow group; weak Lefschetz theorem; intersections K. H. Paranjape, Cohomological and cycle-theoretic connectivity , Ann. of Math. (2) 139 (1994), no. 3, 641-660. JSTOR: | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Schottky problem; Kadomtsev-Petviashvili equation; Jacobian; theta function; Kummer variety | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Diophantine equation; elliptic curves; Mordell Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture; parity conjecture | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curve; rank of the Mordell-Weil group; twists; Galois cohomology | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Betti numbers; Riccati equation; Witten cohomology; intersection numbers; quantum field theory; moduli space of stable holomorphic vector bundles; Hodge-Poincaré polynomial; Harder-Narasimhan recursion | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) arithmetic geometry codes; curves with many rational points; modular curves; class field theory; Deligne-Lusztig curves; infinite global fields; decoding of AG-codes; sphere packings; codes from multidimensional varieties; quantum AG-codes | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) universal Picard variety; universal Jacobian variety; moduli space of smooth curves; relative Néron-Severi group Kouvidakis, A., The Picard group of the universal Picard varieties over the moduli space of curves, J. Differential Geom., 34, 3, 839-850, (1991) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Jacobian variety; theta functions; eta function Couveignes, J-M; Ezome, T, Computing functions on Jacobians and their quotients, LMS J. Comput. Math., 18, 555-577, (2015) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Artinian algebra; parametrization; Hilbert function; homology; Artinian quotients; Grassmannian varieties; determinantal variety; Hankel matrix; homology class of intersection Iarrobino, A., Yameogo, J.: The family \(G\)\_{}\{\(T\)\} of graded quotients of \({k[x,y]}\) of given Hilbert function. arXiv:alg-geom/9709021 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) reductive connected algebraic group; unipotent element; irreducible components; variety of Borel subgroups; irreducible representations; permutation representation; Levi decomposition; irreducible cuspidal representation; Coxeter group; generalized Springer correspondence; special orthogonal groups; intersection cohomology G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205-272. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) arrangement; channel assignment; configuration; Whitney polynomial; Tutte-Grothendieck invariant; graph colouring; intersection theory; Redei functions; geometric lattice; rank function D. J. A. Welsh and G. P. Whittle. Arrangements, channel assignments, and associated polynomials. Adv. in Appl. Math., 23:375--406, 1999. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Picard group; Prym variety; curve with an involution; Brill-Noether theory V. Kanev,special line bundles on curves with involution, Math. Z.222 (1996), 213--229. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) complex smooth quasiprojective algebraic variety; complex linear algebraic group; localization; Mayer-Vietoris sequences; higher \(K\)- theory; weakly \(G\)-equivariant \({\mathcal D}_ X\)-modules; Riemann-Roch theorem; derived categories; Thomason's approximation theorem [J4] Joshua, R.: HigherK-theory of the category weakly equivariantD-modules. Duke Math. J.63, 791--799 (1991) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; intersection of the torsion subgroup; isogenies; zero estimates of transcendence theory M. Hindry , Points de torsion sur les sous-variétés de variétés abéliennes , C.R. Acad. Sci. Paris 304 (1987) Série 1, 311-314. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) potential theory; p-adic dynamics; Berkovich spaces; capacity; equidistribution; Fekete-Szegö theorem; Green's function; rational maps \textsc{M. Baker and R. Rumely}, Potential Theory and Dynamics on the Berkovich Projective Line, Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 2010. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) complex polynomial in two variables; rational function field; rational map Cassou-Noguès, P.: Bad field generators. Contemp. math. 369, 77-83 (2005) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Mordell-Weil group; Selmer group; Birch and Swinnerton-Dyer conjecture; parity conjecture | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) complete intersection; rational homotopy theory; Pontryagin algebra; loop space; homology; Adams-Hilton model | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) towers of function fields; rational places; genus of a function field; automorphisms of function fields; \(p\)-rank | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic curve; number field; function field; Brauer group; local invariants; reciprocity law | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(K3\) surfaces; elliptic curves; fibrations; rational curves; elliptic surfaces; lattices; Dynkin diagrams; Mordell-Weil lattices | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Weierstrass point; Brill-Noether theory; Kodaira dimension; degenerations; smoothings of linear series; moduli space of curves of genus g; monodromy group Eisenbud, D., Harris, J.: The irreducibility of some families of linear series. (Preprint 1984) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fundamental group; Shafarevich conjecture; absolute Galois group; function field; finite split embedding problem; Abhyankar's conjecture Florian Pop, ``Étale Galois covers of affine smooth curves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture'', Invent. Math.120 (1995) no. 3, p. 555-578 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) geometric Langlands program; quantum field theory; Hitchin equation; tame ramification; wild ramification; sigma model; Higgs bundle; electric-magnetic S-duality; affine braid group; hyper-Kähler moduli space E. Witten, Mirror Symmetry, Hitchin's Equations, And Langlands Duality, arXiv:0802.0999 [ INSPIRE ]. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Ramanujan's function $k(\tau)$; modular function; class field theory; congruence subgroup; Rogers-Ramanujan continued fraction; Kronecker's congruence | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hecke ring; Lefschetz fixed point theory; \(\ell \)-adic cohomology; smooth compactification of the Siegel modular variety; étale topology Hatada, K.: Correspondences for Hecke rings and (co-) homology groups on Siegel modular varieties (1988) (preprint). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) affine algebra varieties; quasiprojective varieties; intersection theory; birational equivalence; algebraic groups; degenerations; Bertini theorems; singularities; zeta function Shafarevich I.R.: Basic Algebraic Geometry 1: Varieties in Projective Space. Springer, New York (1988) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) determinant line bundle; vertex operators; loop group; Kac-Moody Lie algebras; affine algebras; infinite-dimensional Lie groups; central extensions; circle group; Grassmannian; polarized Hilbert space; Schubert cell decomposition; homogeneous space; complex manifold; Borel-Weil theory; spin representation; Kac character formula; Bernstein-Gel'fand- Gel'fand resolution | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) equivariant Chow group; intersection product; linear algebraic group action; equivariant intersection theory Angelo Vistoli, \textit{The Chow ring of {M}2, appendix to equivariant intersection theory} {Inventiones Mathematicae}, \textbf{131}, 1996. DOI 10.1007/s002220050214; zbl 0940.14003; MR1614559 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) \(q\)-Whittaker function; finite field; Jordan form; partial flag variety; Burge correspondence; RSK correspondence; preprojective algebra; socle filtration | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Siegel modular variety of genus two; algebraic cycles; special endomorphisms; intersection multiplicities of the cycles at isolated points; special values of derivatives of certain Eisenstein series; metaplectic group Kudla, S. S.; Rapoport, M., Cycles on Siegel threefolds and derivatives of Eisenstein series, Ann. Sci. Éc. Norm. Supér. (4), 33, 695-756, (2000) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Shimura variety associated to an indefinite quaternion algebra over a totally real field; semi-simple local zeta function; automorphic L- functions; purity of the monodromy filtration; local factor Rapoport, M.: On the local zeta function of quaternionic Shimura varieties with bad reduction. Math. Ann. 279, 673--697 (1988) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) double quadric; Fano's threefolds; Picard group; Hilbert scheme; Albanese variety; Jacobian variety | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) theta divisor in the Jacobian of a non-hyperelliptic smooth curve; rank-4 double point; rank-4 quadrics conjecture; generic constructive Torelli theorem; infinitesimal deformation theory for the singularities of theta divisors SMITH (R.) , VARLEY (R.) . - Deformations of theta divisors and the rank 4 quadrics problem , Compositio Math., t. 76, 1990 , n^\circ 3, p. 367-398. Numdam | MR 92a:14025 | Zbl 0745.14012 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) theorem of Deuring and Shafarevich; algebraic function field; modular representation; rank of class group; ramification index R. Gold andM. Madan, An application of a Theorem of Deuring and Safarevic. Math. Z.191, 247-251 (1986). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Selmer group; Mordell-Weil rank; Brauer-Severi varieties | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) function field; rational place; Weierstrass semigroup; tower of function fields Geil O., Matsumoto R.: Bounding the number of \(\mathbb{F}_q\)-rational places in algebraic function fields using Weierstrass semigroups. J. Pure Appl. Algebra \textbf{213}(6), 1152-1156 (2009). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) boundary quantum field theory; renormalization group | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) hypersurfaces; Schebert calculus; cubic hypersurfaces; cubic threefolds; cubic fourfolds; Pfaffian cubics; unirationality; rationality; Picard group; intermediate Jacobian; Albanese variety; Abel-Jacobi map; conic bundles; abelian varieties; Prym varieties; Hilbert square; varieties with vanishing Chern class; Calabi-Yau varieties; holomorphic symplectic varieties; Beauville-Bogomolov decomposition theorem | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) ground field extension; principally polarized Jacobian variety [23]K. Sekino and T. Sekiguchi, On the fields of definition for a curve and its Jacobian variety, Bull. Fac. Sci. Engrg. Chuo Univ. Ser. I Math. 31 (1988), 29--31. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Artin invariant; Mordell-Weil groups of quasi-elliptic surfaces; rational unirational quasi-elliptic surfaces; characteristic 3; Néron-Severi groups; K3 surfaces Hiroyuki Ito, The Mordell-Weil groups of unirational quasi-elliptic surfaces in characteristic 3, Math. Z. 211 (1992), no. 1, 1 -- 39. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) toric variety; intersection theory; Chow cohomology classes; Minkowski weight; Kronecker duality; Chow rings; polytope algebra W. Fulton and B. Sturmfels, ''Intersection Theory on Toric Varieties,'' Topology 36, 335--353 (1997). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) fat points; projective plane; Weyl group; graded Betti number; Hilbert function; rational surface Harbourne, B., The ideal generation problem for fat points, J. Pure Appl. Algebra, 145, 165-182, (2000) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) real algebraic variety; rational function; rational representation; semialgebraic function; Nash function | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) height function; unipotent flows; rational points; projective algebraic variety [26] Oh (H.).-- Orbital counting via mixing and unipotent flows. In ''Homogeneous flows, moduli spaces and arithmetic'', M. Einsiedler et al eds., Clay Math. Proc. 10, Amer. Math. Soc., p.~339-375 (2010). &MR~26 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil rank of the jacobians; superelliptic curves; Mordell-Weil group Murabayashi, N.: Mordell -- Weil rank of the Jacobians of the curves defined by \(yp=f(x)\). Acta arith. 64, No. 4, 297-302 (1993) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Monge-Ampère operator; Riemann-Zariski space; Weil divisor; nef Weil divisors; intersection theory Boucksom, Sébastien; Favre, Charles; Jonsson, Mattias, Valuations and plurisubharmonic singularities, Publ. Res. Inst. Math. Sci., 44, 2, 449-494, (2008) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abelian variety; finite field; Weil numbers F. Oort, ''Abelian varieties over finite fields,'' in Higher-Dimensional Geometry over Finite Fields, Amsterdam: IOS, 2008, vol. 16, pp. 123-188. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil group; elliptic curves; elliptic surfaces Naskręcki, B., Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples, Acta arith., 160, 2, 159-183, (2013) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) group scheme; Picard group; global function field; cohomology; Tate-Shafarevich set | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hasse norm principle; class field theory; rational points on varieties; harmonic analysis | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Jacobian variety; characteristic polynomial of the Frobenius; rational points | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) formally real function field; real holomorphy ring; finitely generated ideal; group of invertible fractional ideals Kucharz, W.: Invertible ideals in real holomorphy rings. J. reine angew. Math. 395, 171-185 (1989) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) abstract intersection theory; Riemann hypothesis; complex field; Dirichlet \(L\)-function; Dirichlet character; \(l\)-adic cohomology; finite field; Gelfand-Naimark-Segal representation | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Shimura variety; zeta function; unitary group; affine flag variety; local model; perverse sheaf | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) global field of positive characteristic; Langlands conjecture; \(\ell\)-adic representations; Weil group; automorphic cuspidal representations; adele , Two dimensional /-adic representations of the Galois group of a global field of characteristic/? and automorphic forms on GL(2), J. Soviet Math., 36, No. 1 (1987), 93-105. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) hypergeometric function; Hodge cycle; Jacobian variety H. Movasati, S. Reiter, Hypergeometric series and Hodge cycles of four dimensional cubic hypersurfaces. Preprint math.AG/0507436 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) congruence function field; automorphism group; Galois group; ramification | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Kloosterman equations; affine algebraic groups; motifs; Hodge theory; differential Galois group; ordinary differential field; Tannakian categories N. M. Katz, ''On the calculation of some differential Galois groups,'' Invent. Math., vol. 87, iss. 1, pp. 13-61, 1987. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) connected reductive linear algebraic group; variety of Borel subgroups; Lie algebra; Weil conjecture; Frobenius endomorphism; \(\ell \)-adic cohomology group; eigenvalues Springer, T.A.: A purity result for fixed point varieties in flag manifolds. J.~Fac.~Sci.~Univ.~Tokyo Sect.~IA, Math.~\textbf{31}, 271-282 (1984) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) meromorphic function; cusp forms; functional equation; Mellin transforms; Rankin type convolution; generalized period; Jacobian variety | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) linear algebraic group; nilpotent variety; normality; Borel-Bott-Weil theorem; vanishing results; positive characteristics Jesper Funch Thomsen, Normality of certain nilpotent varieties in positive characteristic, J. Algebra 227 (2000), no. 2, 595-613. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) root system; fan; toric variety; cohomology; vector bundle; point over a finite field Gashi, Q.: A vanishing result for toric varieties associated with root systems, Albanian J. Math. 1, 235-244 (2007) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) complete intersection point; Chow group; Hilbert scheme; projectively generated ideal; CI points; maximal ideals; Murthy ring; \(K_ 0\) [W1]C. Weibel: ``Complete intersection points on affine varieties{'' Comm. in Algebra 12 (24) (1984) pp. 3011--3051.} | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) generalized Weil's reciprocity law; one-dimensional group variety; topology of the fiber-structure; invariant of homomorphism; Riemann surface | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cyclotomic unit; arithmetic of an elliptic curve; Mordell-Weil group; Tate-Shafarevich group; Birch and Swinnerton-Dyer conjecture; Weil curves; Selmer group; family of Heegner points; elliptic units V. A. KOLYVAGIN, The Mordell-Weil and Shafarevich-Tate groups for Weil elliptic curves. (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 52, no. 6 (1988), pp. 1154-1180, 1327; translation in Math. USSR-Izv., 33, no. 3 (1989), pp. 473-499. Zbl0681.14016 MR984214 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Hilbert modular variety; Hilbert modular group; Hecke operator; local zeta function K. Hatada: On the local zeta functions of the Hilbert modular schemes. Proc. Japan Acad., 66A, 195-200 (1990). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) equivalence problem; minimal rational curve; complete intersection; variety of minimal rational tangents (VMRT) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) basis for cohomology group; irreducible module; semisimple linear algebraic group; Borel subgroup; Schubert variety; standard monomial theory Seshadri, C. S.: Standard monomial theory and the work of Demazure. Advanced studies in pure mathematics 1 (1982) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) affine variety; group of automorphisms; fixed point of a polynomial automorphism | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) factorization of birational maps; minimal rational surfaces; Mori theory; Cremona group; extremal contractions Исковских, В. А., Факторизация бирациональных отображений рациональных поверхностей с точки зрения теории мори, УМН, 51, 4-310, 3-72, (1996) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) zero estimates; commutative group variety; multiplicity; multiprojective varieties; Baker's theory; linear forms in logarithms; algebraic groups; derivations along one-parameter subgroup; multihomogeneous polynomials [15]D. Masser and G. W\"{}ustholz, Zero estimate on group varieties II, Invent. Math. 80 (1985), 233--267. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) cubic surface; rational points; height; counting function; Manin's conjecture; smallest point; Peyre constant; numerical computation Elsenhans, A. -S.; Jahnel, J.: Experiments with general cubic surfaces, Progr. math. 269, 637-654 (2007) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Mordell-Weil group; torsion group | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) De Rham cohomology; crystalline action of Weil group; Morita's \(p\)-adic gamma function; absolute Hodge cycles; Frobenius matrix of Fermat curves Ogus, A, A \(p\)-adic analogue of the chowla-Selberg formula, \(p\)-adic analysis (Trento, 1989), Lect. Notes Math., 1454, 319-341, (1990) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) trigonal curve; rationality; unirationality; total ramification point; moduli scheme of trigonal curves; rational variety Casnati G., Del Centina A.: On certain loci of curves of genus g 4 with Weierstrass points whose first non-gap is three. Math. Proc. Cambridge Philos. Soc. 132, 395--407 (2002) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curve; Selmer group; Mordell-Weil group | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Seshadri lemma; invariant function; algebraic group acting on irreducible affine variety Popov, V. L.: On the ''lemma of Seshadri, Adv. soviet math. 8, 133-139 (1992) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) nilpotent Hessenberg variety; intersection theory; Lie algebra; Schubert variety; singularity Insko, Erik; Tymoczko, Julianna, Intersection theory of the Peterson variety and certain singularities of Schubert varieties, Geom. Dedicata, 180, 95-116, (2016) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil group E. Artal Bartolo, H. Tokunaga, and D. Zhang, Miranda--Persson's problem on extremal elliptic \(K3\) surfaces, Pacific J. Math. 202 (2002), 37--72. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) arithmetic abelian scheme; abelian variety; Fourier transformation; intersection pairing; rational Arakelov-Chow groups Bachmat, E. : A Fourier transform construction for Arakelov Chow groups of arithmetic abelian schemes . Duke Math. J., Int. Math. Res. Notices, No. 7, (1993), 227-232. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) divisor class group; rational double point; rational singularities; simplicial toric surface; symbolic powers; uniform symbolic topologies Walker, R. M., Rational singularities and uniform symbolic topologies, Illinois J. Math., 60, 2, 541-550, (2016) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) binary quartic forms; \(K3\) surface; elliptic fibration; Mordell-Weil group Masato Kuwata, Elliptic fibrations on quartic \?3 surfaces with large Picard numbers, Pacific J. Math. 171 (1995), no. 1, 231 -- 243. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil group S. Kitagawa, Extremal hyperelliptic fibrations on rational surfaces, Saitama Math. J. 30 (2013), 1--14. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Mordell-Weil lattices; elliptic curve; Mordell-Weil group Usui, H.: On Mordell-Weil lattices of type D5. Math. Nachrichten (to appear). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) structure of group rational points; isogeny; elliptic curve over finite field J. F. Voloch, ''A note on elliptic curves over finite fields,'' Bull. Soc. Math. France 116(4), 455--458 (1988). | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) infinite regular Galois covering curves; rational geometric fundamental group with base point Gerhard Frey, Ernst Kani, and Helmut Völklein, Curves with infinite \?-rational geometric fundamental group, Aspects of Galois theory (Gainesville, FL, 1996) London Math. Soc. Lecture Note Ser., vol. 256, Cambridge Univ. Press, Cambridge, 1999, pp. 85 -- 118. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) torsion subgroup of Galois group; Iwasawa theory; elliptic curves; imaginary quadratic field; \({bbfZ}_{\ell }\)-extension; abelian extension; maximal abelian p-extension | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Fano variety; anticanonical divisor; pseudoindex; Mori's theory; family deformation of a rational curve Wiśniewski, J., On a conjecture of Mukai, Manuscripta Math., 68, 135-141, (1990) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) theory of algebraic curves; coding theory; Riemann-Roch theorem; function fields; differentials; Hasse-Weil theorem; geometric Goppa codes; trace codes H. Stichtenoth, Algebraic Function Fields and Codes, Second edn, (Springer-Verlag, Berlin Heidelberg, 2009). Zbl0816.14011 MR2464941 | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) algebraic curves; rational points; global function field; asymptotic bound Xing, C.; Yeo, S. L., Algebraic curves with many points over the binary field, J. Algebra, 311, 775-780, (2007) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) tame ramification; Coates algorithm; elements of bounded norm; global function field; reduced integral bases; Puiseux series; Riemann-Roch space; successive minima; unit group; torsion units; root tests Schörnig, M., 1996. Untersuchungen konstruktiver Probleme in globalen Funktionenkörpern. Thesis. TU Berlin | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) compensated convex transforms; mathematical morphology; non-flat morphological operators; convex envelope; Moreau envelope; characteristic function; point clouds; Hausdorff-Lipschitz continuity; surface-to-surface intersection; transversal intersections; random samples K. Zhang, A. Orlando, and E. Crooks, \textit{Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds}, Math. Models Methods Appl. Sci., 25 (2015), pp. 839--873. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Kummer extension; rational function field; splitting of prime divisors; genus; smooth projective curve Xing, C. P.: Multiple Kummer Extensions and the Number of Prime Divisors of Degree One in Function Fields. J. of Pure and Appl. Algebra84, 85--93 (1993) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) Picard integrals; transcendental point; jacobian; abelian variety of CM- type R.-P. Holzapfel, Transcendental Ball Points of Algebraic Picard Integrals, \textit{Math. Nachr.}, \textbf{161} (1993), 7-25. | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) rational function field; maximal rational subfield; birational invariant Yoshihara, H., \textit{degree of irrationality of hyperelliptic surfaces}, Algebra Colloq., 7, 319-328, (2000) | 0 |
rational point; function field; Jacobian variety; Mordell-Weil group; intersection theory Shioda, T.: Mordell-Weil lattices for higher genus fibration over a curve. In: New Trends in Algebraic Geometry (Warwick 1996), pp. 359-373, London Mathematical Soceity, Lecture Note on Series , vol. \textbf{264}. Cambridge University Press, Cambridge (1999) elliptic curves; Mordell-Weil group | 0 |
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