Growth of Sha in towers for isogenous curves

Tim Dokchitser, Vladimir Dokchitser

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)
33 Downloads (Pure)


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.
Original languageEnglish
JournalCompositio Mathematica
Early online date30 Jun 2015
Publication statusE-pub ahead of print - 30 Jun 2015

Bibliographical note

28 pages


  • math.NT
  • 11G07 (Primary), 11G05, 11G10, 11G40, 11R23 (Secondary)


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