scientific article

zbMath0753.14025MaRDI QIDQ4012045

Victor Kolyvagin

Publication date: 27 September 1992

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zbMATH Keywords

Tate-Shafarevich groupHeegner pointsmodular elliptic curve

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Elliptic curves (14H52) Modular and Shimura varieties (14G35) Galois cohomology (11R34) Elliptic and modular units (11G16)

Related Items (13)

Kolyvagin’s Work on Modular Elliptic Curves ⋮ There are genus one curves over \mathbb{Q} of every odd index ⋮ Exhibiting SHA[2 on hyperelliptic Jacobians] ⋮ Kolyvagin's result on the vanishing of \(\Sha(E/K)[p^\infty\) and its consequences for anticyclotomic Iwasawa theory] ⋮ Structure of Tate-Shafarevich groups of elliptic curves over global function fields ⋮ On the structure of Selmer and Shafarevich–Tate groups of even weight modular forms ⋮ Solvable points on genus one curves ⋮ On the structure of Selmer groups ⋮ Explicit Heegner points: Kolyvagin's conjecture and non-trivial elements in the Shafarevich-Tate group ⋮ A BSD formula for high-weight modular forms ⋮ Algorithms for the arithmetic of elliptic curves using Iwasawa theory ⋮ Vanishing of some cohomology groups and bounds for the Shafarevich-Tate groups of elliptic curves ⋮ Kolyvagin's work and anticyclotomic tower fields: the supersingular case

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