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Growth of
$\unicode[STIX]{x0428}$ in towers for isogenous curves
Published online by Cambridge University Press: 30 June 2015
Abstract
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.
Keywords
- Type
- Research Article
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- Copyright
- © The Authors 2015
References
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