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On the automorphy of l-adic Galois representations with small residual image With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Jack Thorne

Part of: Discontinuous groups and automorphic forms Algebraic number theory: global fields

Published online by Cambridge University Press:  05 April 2012

Jack Thorne
Jack Thorne
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA ([email protected])
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Abstract

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into GLn. Existing theorems require that the residual representation have ‘big’ image, in a certain technical sense. Our theorems are based on a strengthening of the Taylor–Wiles method which allows one to weaken this hypothesis.

Keywords

Galois representationsGalois cohomologyrepresentation theory of p-adic groups

MSC classification

Secondary: 11F80: Galois representations 11R34: Galois cohomology
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 4 , October 2012 , pp. 855 - 920
Copyright
Copyright © Cambridge University Press 2012

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