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)