Analytic families of finite-slope Selmer groups

Pottharst, Jonathan

doi:10.2140/ant.2013.7.1571

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Analytic families of finite-slope Selmer groups

Jonathan Pottharst

Vol. 7 (2013), No. 7, 1571–1612

DOI: 10.2140/ant.2013.7.1571

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 $(φ, Γ)$ -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

Milestones

Received: 17 August 2011

Revised: 28 July 2012

Accepted: 17 December 2012

Published: 12 October 2013

Authors

Jonathan Pottharst
Department of Mathematics and Statistics Boston University 111 Cummington Mall Boston, MA 02215 United States

Vol. 7, No. 7, 2013