Abstract
We prove an automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call \potentential diagonalizability. This result allows for \change of weight and seems to be substantially more exible than previous theorems along the same lines. We derive several applications. For instance we show that any irreducible, totally odd, essentially self-dual, regular, weakly compatible system of l-adic representations of the absolute Galois group of a totally real eld is potentially automorphic and hence is pure and its L-function has meromorphic continuation to the whole complex plane and satises the expected functional equation.
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