Vol. 7, No. 7, 2013

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Analytic families of finite-slope Selmer groups

Jonathan Pottharst

Vol. 7 (2013), No. 7, 1571–1612
Abstract

We develop a theory of Selmer groups for analytic families of Galois representations, which are only assumed “ordinary” on the level of their underlying $\left(\phi ,\Gamma \right)$-modules. Our approach brings the finite-slope nonordinary case of Iwasawa theory onto an equal footing with ordinary cases in which $p$ is inverted.

Keywords
Iwasawa theory, Selmer group, families of Galois representations, $(\varphi, \Gamma)$-modules
Mathematical Subject Classification 2010
Primary: 11R23
Secondary: 11R34, 12G05