Local-global compatibility for $l=p$, II

By Thomas Barnet-Lamb, T. Gee, David Geraghty, Richard Taylor. 2011

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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 GL_n 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.

Subfields: Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/62b7f5468565f3f98f954750fa57537a500af295