English

Locally trivial torsors that are not Weil-Ch\^atelet divisible

Number Theory 2015-12-18 v2

Abstract

For every prime p we give infinitely many examples of torsors under abelian varieties over Q that are locally trivial but not divisible by p in the Weil-Ch\^atelet group. We also give an example of a locally trivial torsor under an elliptic curve over Q which is not divisible by 4 in the Weil-Ch\^atelet group. This gives a negative answer to a question of Cassels.

Keywords

Cite

@article{arxiv.1206.2420,
  title  = {Locally trivial torsors that are not Weil-Ch\^atelet divisible},
  author = {Brendan Creutz},
  journal= {arXiv preprint arXiv:1206.2420},
  year   = {2015}
}

Comments

v2: updated/corrected bibliography