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Growth of
$\unicode[STIX]{x0428}$ in towers for isogenous curves
- Part of
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- Journal:
- Compositio Mathematica / Volume 151 / Issue 11 / November 2015
- Published online by Cambridge University Press:
- 30 June 2015, pp. 1981-2005
- Print publication:
- November 2015
-
- Article
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We study the growth of
$\unicode[STIX]{x0428}$ and 
$p^{\infty }$-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 ‘positive 
${\it\mu}$-invariant’ setting in the Iwasawa theory of elliptic curves. The towers we consider are 
$p$-adic and 
$l$-adic Lie extensions for 
$l\neq p$, in particular cyclotomic and other 
$\mathbb{Z}_{l}$-extensions.
