Local-global compatibility for l=p, II
  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. 
Thomas Barnet-Lamb, Toby Gee, David Geraghty, Richard Taylor
math.NT