Local-global compatibility for l=p, II
Abstract
We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GLn over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.
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