English

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}
}

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28 pages