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Local-global compatibility for l = p , I

Thomas Barnet-Lamb;  Toby Gee;  David Geraghty;  Richard Taylor — 2012

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the compatibility of the local and global Langlands correspondences at places dividing l for the l -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of GL n over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing l and have Shin-regular weight.

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