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