English

Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

Number Theory 2019-02-20 v2

Abstract

For an abelian variety A over a number field k we discuss the maximal divisibile subgroup of H^1(k,A) and its intersection with the subgroup Sha(A/k). The results are most complete for elliptic curves over Q.

Keywords

Cite

@article{arxiv.1106.4255,
  title  = {Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q},
  author = {Mirela Çiperiani and Jakob Stix},
  journal= {arXiv preprint arXiv:1106.4255},
  year   = {2019}
}

Comments

22 pages, changed title, the origional manuscript arXiv:1106.4255v1 was split in two parts according to Div-questions (part I) and div-questions (part II: Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups II: On a question of Cassels)

R2 v1 2026-06-21T18:25:35.827Z