a1 Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA (firstname.lastname@example.org)
We prove new automorphy lifting theorems for essentially conjugate self-dual Galois representations into GL n . 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.
(Received October 13 2010)
(Received January 13 2011)
(Accepted January 25 2011)
AMS 2010 Mathematics subject classification