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Arbitrarily large 2-torsion in Tate–Shafarevich groups of abelian varieties

Volume 191 / 2019

E. V. Flynn Acta Arithmetica 191 (2019), 101-114 MSC: Primary 11G30; Secondary 11G10, 14H40. DOI: 10.4064/aa171118-7-12 Published online: 5 September 2019

Abstract

We show that, for any $d$, the $2$-torsion of Tate–Shafarevich groups of absolutely simple abelian varieties of dimension $d$ over $\mathbb Q $ can be arbitrarily large. This involves the use of an approach, which we shall describe, for demonstrating arbitrarily large Tate–Shafarevich groups which does not require entire Selmer groups to be found.

Authors

  • E. V. FlynnMathematical Institute
    University of Oxford
    Andrew Wiles Building
    Radcliffe Observatory Quarter, Woodstock Road
    Oxford OX2 6GG
    United Kingdom
    e-mail

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