Derived heights and generalized Mazur-Tate regulators

DOI10.1215/S0012-7094-94-07604-7zbMath0853.14013OpenAlexW2074523661MaRDI QIDQ1345226

Henri Darmon, Massimo Bertolini

Publication date: 6 January 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07604-7

zbMATH Keywords

\(L\)-functionBirch-Swinnerton-Dyer conjecture\(\theta\)-elementgeneralized Mazur-Tate regulator

Mathematics Subject Classification ID

Elliptic curves (14H52) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Other algebras and orders, and their zeta and (L)-functions (11R54)

Related Items (14)

On the nonvanishing of generalised Kato classes for elliptic curves of rank 2 ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil L-functions, III ⋮ A refined Beilinson–Bloch conjecture for motives of modular forms ⋮ Congruences and rationality of Stark-Heegner points ⋮ Congruences for critical values of higher derivatives of twisted Hasse–Weil $L$-functions, II ⋮ Comparing anticyclotomic Selmer groups of positive coranks for congruent modular forms. II ⋮ Unnamed Item ⋮ Iwasawa theory for elliptic curves over imaginary quadratic fields ⋮ On anticyclotomic variants of the \(p\)-adic Birch and Swinnerton-Dyer conjecture ⋮ Organizing the arithmetic of elliptic curves ⋮ On the anticyclotomic Iwasawa main conjecture for modular forms ⋮ Toric Regulators ⋮ \(\Lambda\)-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves ⋮ On the freeness of anticyclotomic Selmer groups of modular forms

Cites Work

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• Iwasawa L-functions of varieties over algebraic number fields. A first approach
• Galois properties of points of finite order of elliptic curves
• Rational points of Abelian varieties with values in towers of number fields
• Arithmetic on Curves of Genus 1 : III. The Tate-Šafarevič and Selmer Groups
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• On construction of holomorphic cusp forms of half integral weight

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