A converse to a theorem of Gross, Zagier, and Kolyvagin

DOI10.4007/annals.2020.191.2.1zbMath1447.11071arXiv1405.7294OpenAlexW3006636502MaRDI QIDQ2296294

Christopher M. Skinner

Publication date: 18 February 2020

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.7294

zbMATH Keywords

Iwasawa theoryHeegner pointsBirch-Swinnerton-Dyer conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Elliptic curves over local fields (11G07)

Related Items (21)

The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ Elliptic curves of rank two and generalised Kato classes ⋮ Hirzebruch-Zagier cycles and twisted triple product Selmer groups ⋮ On the nonvanishing of generalised Kato classes for elliptic curves of rank 2 ⋮ Plectic \(p\)-adic invariants ⋮ On the soft \(p\)-converse to a theorem of Gross-Zagier and Kolyvagin ⋮ The congruent number problem and elliptic curves ⋮ INDIVISIBILITY OF HEEGNER CYCLES OVER SHIMURA CURVES AND SELMER GROUPS ⋮ A \(p\)-adic Waldspurger formula and the conjecture of Birch and Swinnerton-Dyer ⋮ The even parity Goldfeld conjecture: congruent number elliptic curves ⋮ A proof of Perrin-Riou's Heegner point main conjecture ⋮ Anticyclotomic \(p\)-adic \(L\)-functions and Ichino's formula ⋮ Heegner point Kolyvagin system and Iwasawa main conjecture ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and a conjecture of Perrin-riou ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ Rubin's conjecture on local units in the anticyclotomic tower at inert primes ⋮ On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes ⋮ On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves

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