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.
Bibliographical note28 pages
- 11G07 (Primary), 11G05, 11G10, 11G40, 11R23 (Secondary)