Elements of class groups and Shafarevich-Tate groups of elliptic curves
From MaRDI portal
Publication:1420209
DOI10.1215/S0012-7094-03-12012-8zbMath1048.11044OpenAlexW2039187921MaRDI QIDQ1420209
Publication date: 28 January 2004
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/s0012-7094-03-12012-8
Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)
Related Items (7)
Elements of prime order in Tate–Shafarevich groups of abelian varieties over ⋮ Ideal class groups of imaginary quadratic fields ⋮ Divisibility of class numbers of imaginary quadratic fields whose discriminant has only three prime factors ⋮ Divisibility of class numbers of imaginary quadratic fields whose discriminant has only two prime factors ⋮ Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families ⋮ Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion points ⋮ Imaginary quadratic fields with 2-class group of type \((2,2^\ell)\)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Fourier coefficients and modular forms of half-integral weight
- Sur les coefficients de Fourier des formes modulaires de poids demi-entier
- Non-vanishing of quadratic twists of modular \(L\)-functions
- Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication
- Selmer groups of quadratic twists of elliptic curves
- Nonvanishing of \(L\)-series and the combinatorial sieve. With an appendix by David E. Rohrlich: Unboundedness of the Tate-Shafarevich group in families of quadratic twists
- 5-torsion in the Shafarevich-Tate group of a family of elliptic curves
- Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
- Goldbach numbers represented by polynomials
- On modular forms of half integral weight
- Nonvanishing of quadratic twists of modular L-functions and applications to elliptic curves
- A Family of Semistable Elliptic Curves with Large Tate-Shafarevitch Groups
- On the Selmer Group of Twists of Elliptic Curves with Q-Rational Torsion Points
- Die Ordnung der Schafarewitsch‐Tate‐Gruppe kann beliebig groß werden
- Divisibility of Class Numbers of Imaginary Quadratic Fields
- Additive representation in thin sequences, II: The binary Goldbach problem
- On Ranks of Twists of Elliptic Curves and Power-Free Values of Binary Forms
- The Square-Free Sieve and the Rank of Elliptic Curves
- A Generalization of the Siegel-Walfisz Theorem
- On the density of discriminants of cubic fields. II
- Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.
This page was built for publication: Elements of class groups and Shafarevich-Tate groups of elliptic curves
