ARBITRARILY LARGE p-TORSION IN TATE-SHAFAREVICH GROUPS

E. Victor Flynn; Ari Shnidman; Tom Fisher

doi:10.1017/S1474748024000392

ARBITRARILY LARGE p-TORSION IN TATE-SHAFAREVICH GROUPS

E. Victor Flynn
, Ari Shnidman
, Tom Fisher

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that, for any prime p, there exist absolutely simple abelian varieties over with arbitrarily large p-torsion in their Tate-Shafarevich groups. To prove this, we construct explicit -covers of Jacobians of curves of the form which violate the Hasse principle. In the appendix, Tom Fisher explains how to interpret our proof in terms of a Cassels-Tate pairing.

Original language	English
Pages (from-to)	481-502
Number of pages	22
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	24
Issue number	2
DOIs	https://doi.org/10.1017/S1474748024000392
State	Published - 1 Mar 2025

Bibliographical note

Publisher Copyright:
© 2024 The Author(s).

Keywords

Tate-Shafarevich group
abelian variety

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10.1017/S1474748024000392

Cite this

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ARBITRARILY LARGE p-TORSION IN TATE-SHAFAREVICH GROUPS

Abstract

Bibliographical note

Keywords

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