Journal of the Institute of Mathematics of Jussieu

Research Article

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

Jack Thornea1

a1 Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA 02138, USA (


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)


  • Galois representations;
  • Galois cohomology;
  • representation theory of p-adic groups

AMS 2010 Mathematics subject classification

  • Primary 11F80;
  • 11R34