Growth of Sha in towers for isogenous curves
Number Theory
2015-12-02 v1
Abstract
We study the growth of the Tate-Shafarevich and p-infinity Selmer groups for isogenous abelian varieties in towers of number fields, with an emphasis on elliptic curves. The growth types are usually exponential, as in the setting of `positive mu-invariant' in Iwasawa theory of elliptic curves. The towers we consider are p-adic and l-adic Lie extensions for l<>p, in particular cyclotomic and other Z_l-extensions.
Keywords
Cite
@article{arxiv.1301.4257,
title = {Growth of Sha in towers for isogenous curves},
author = {Tim Dokchitser and Vladimir Dokchitser},
journal= {arXiv preprint arXiv:1301.4257},
year = {2015}
}
Comments
28 pages