English

Potential Sha for abelian varieties

Number Theory 2015-12-18 v2

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.

Keywords

Cite

@article{arxiv.1010.3349,
  title  = {Potential Sha for abelian varieties},
  author = {Brendan Creutz},
  journal= {arXiv preprint arXiv:1010.3349},
  year   = {2015}
}

Comments

Version 2: improved exposition and corrected various small errors

R2 v1 2026-06-21T16:29:28.196Z