Visibility of Shafarevich-Tate groups of abelian varieties.

DOI10.1006/jnth.2002.2810zbMath1101.14055OpenAlexW2117791557MaRDI QIDQ1867431

Amod Agashe, William A. Stein

Publication date: 2 April 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.2002.2810

zbMATH Keywords

conjectureShafarevich-Tate groupvisibilitymodular abelian varietyBirch and Swinnerton-Dyer

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Arithmetic ground fields for abelian varieties (14K15)

Related Items

Local solubility and height bounds for coverings of elliptic curves, Exhibiting SHA[2 on hyperelliptic Jacobians], Visualising Sha[2 in Abelian surfaces], Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero, Computing the Cassels-Tate pairing on the Selmer group of a Richelot isogeny, Visualizing elements of order in the Tate–Shafarevich group of an elliptic curve, Visualizing elements of order two in the Weil-Châtelet group, Visibility of ideal classes, Relating the Tate-Shafarevich group of an elliptic curve with the class group, Visibility and the Birch and Swinnerton-Dyer conjecture for analytic rank zero, Algorithms for the arithmetic of elliptic curves using Iwasawa theory

Uses Software

• Magma
• ecdata

Cites Work

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