Potential Sha for abelian varieties

Abstract

We show that the p-torsion in the Tate-Shafarevich group of any principally polarized abelian variety over a number field is unbounded as one ranges over extensions of degree O(p), the implied constant depending only on the dimension of the abelian variety.

Version 2: improved exposition and corrected various small errors

References in corpus (1)

• The period-index problem in WC-groups II: abelian varieties

Cited by in corpus (4)

• The growth of fine Selmer groups
• Selmer groups and class groups
• $p$-Selmer growth in extensions of degree $p$
• Elements of prime order in Tate-Shafarevich groups of abelian varieties over $\mathbb{Q}$