Vol. 6, No. 3, 2012

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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
Abstract

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

Keywords
Galois representations
Primary: 11F80
Milestones
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