Galois representations associated with unitary groups over ℚ

Skinner, Christopher

doi:10.2140/ant.2012.6.1697

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Galois representations associated with unitary groups over $\mathbb Q$

Christopher Skinner

Vol. 6 (2012), No. 8, 1697–1717

DOI: 10.2140/ant.2012.6.1697

Abstract

We show that a cuspidal automorphic representation $π = \otimes_{ℓ \leq \infty} π_{ℓ}$ of a unitary similitude group $GU {(a, b)}_{∕ ℚ}$ with archimedean component $π_{\infty}$ in a regular discrete series has an associated $(a + b)$ -dimensional $p$ -adic Galois representation with Frobenius eigenvalues given by the local base change parameters for all primes $ℓ$ such that $π_{ℓ}$ and $GU (a, b)$ are unramified.

Keywords

Galois representations, unitary groups, automorphic representations

Mathematical Subject Classification 2010

Primary: 11F80

Secondary: 11F70, 11F66

Milestones

Received: 31 March 2011

Accepted: 21 July 2011

Published: 14 December 2012

Authors

Christopher Skinner
Department of Mathematics Princeton University Fine Hall Washington Road Princeton, NJ 08544-1000 United States

Vol. 6, No. 8, 2012