Resumen de Potential automorphy and change of weight

Thomas Barnet Lamb, Toby Gee, David Geraghty, Richard Taylor

• 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 flexible 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 field is potentially automorphic and hence is pure and its L -function has meromorphic continuation to the whole complex plane and satisfies the expected functional equation