Local-global compatibility for , I
Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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We prove the compatibility of the local and global Langlands correspondences at places dividing for the -adic Galois representations associated to regular algebraic conjugate self-dual cuspidal automorphic representations of over an imaginary CM field, under the assumption that the automorphic representations have Iwahori-fixed vectors at places dividing and have Shin-regular weight.