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.Comment: 13 page
