The image of complex conjugation in l-adic representations associated to automorphic forms

Taylor, Richard

doi:10.2140/ant.2012.6.405

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The image of complex conjugation in $l$-adic representations associated to automorphic forms

Richard Taylor

Vol. 6 (2012), No. 3, 405–435

DOI: 10.2140/ant.2012.6.405

Abstract

If $F^{+}$ is a totally real field, if $n$ is an odd integer and if $Π$ is a regular, algebraic, essentially self-dual, cuspidal automorphic representation of ${GL}_{n} (A_{F^{+}})$ , then we calculate the image of any complex conjugation under the $l$ -adic representations $r_{l, ι} (Π)$ associated to $Π$ .

Keywords

Galois representations

Mathematical Subject Classification 2000

Primary: 11F80

Milestones

Received: 29 April 2010

Revised: 2 January 2011

Accepted: 20 February 2011

Published: 5 July 2012

Authors

Richard Taylor
Department of Mathematics Harvard University One Oxford Street Cambridge, MA 02138 United States
http://www.math.harvard.edu/~rtaylor

Vol. 6, No. 3, 2012