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