On the automorphy of $l$-adic Galois representations with small residual image

Mathematics – Number Theory

Scientific paper

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59 pages. To appear in the Journal of the Institute of Mathematics of Jussieu

Scientific paper

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.

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