(p,p)-Galois representations attached to automorphic forms on GL_n

Eknath Ghate and Narasimha Kumar

Vol. 252 (2011), No. 2, 379–406

DOI: 10.2140/pjm.2011.252.379

Abstract

We study the local reducibility at p of the p-adic Galois representation attached to a cuspidal automorphic representation of GL_n(𝔸_ℚ). In the case that the underlying Weil–Deligne representation is Frobenius semisimple and indecomposable, we analyze the reducibility completely. We use methods from p-adic Hodge theory, and work under a transversality assumption on the Hodge and Newton filtrations in the corresponding filtered module.

Keywords

local Galois representation, automorphic representation, filtered module, p-adic Hodge theory

Mathematical Subject Classification 2010

Primary: 11F80

Milestones

Received: 8 September 2010

Revised: 17 January 2011

Accepted: 20 January 2011

Published: 29 October 2011