Semistable periods of finite slope families

Liu, Ruochuan

doi:10.2140/ant.2015.9.435

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Semistable periods of finite slope families

Ruochuan Liu

Vol. 9 (2015), No. 2, 435–458

DOI: 10.2140/ant.2015.9.435

Abstract

We introduce the notion of finite slope families to encode the local properties of the $p$ -adic families of Galois representations appearing in the work of Harris, Lan, Taylor and Thorne on the construction of Galois representations for (non-self-dual) regular algebraic cuspidal automorphic representations of $GL (n)$ over CM fields. Our main result is to prove the analytic continuation of semistable (and crystalline) periods for such families.

Keywords

finite slope families, semistable, $(\varphi,\Gamma)$-modules

Mathematical Subject Classification 2010

Primary: 11F80

Milestones

Received: 11 February 2014

Revised: 9 December 2014

Accepted: 14 January 2015

Published: 5 March 2015

Authors

Ruochuan Liu
Beijing International Center for Mathematical Research Peking University Beijing, 100871 China

Vol. 9, No. 2, 2015