A refined conjecture of Mazur-Tate type for Heegner points

DOI10.1007/BF01231327zbMath0781.11023WikidataQ123135438 ScholiaQ123135438MaRDI QIDQ1209128

Henri Darmon

Publication date: 16 May 1993

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144045

zbMATH Keywords

Heegner pointsGalois modulerank of a modular elliptic curve

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Theta functions and curves; Schottky problem (14H42) Elliptic and modular units (11G16)

Related Items

Derived heights and generalized Mazur-Tate regulators ⋮ Elliptic curves of rank two and generalised Kato classes ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil L-functions, III ⋮ On the rank-part of the Mazur-Tate refined conjecture for higher weight modular forms ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ On the structure of Selmer and Shafarevich–Tate groups of even weight modular forms ⋮ On the Kolyvagin cup product ⋮ On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture ⋮ On the passage from local to global in number theory

Cites Work

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• Stable augmentation quotients of Abelian groups
• Heegner points and derivatives of \(L\)-series
• Refined conjectures of the ``Birch and Swinnerton-Dyer type
• On the ideal class groups of real abelian number fields
• Group rings and their augmentation ideals
• Arithmetic of Weil curves
• Galois properties of points of finite order of elliptic curves
• Kolyvagin's descent and Mordell-Weil groups over ring class fields.