  We prove the compatibility of local and global Langlands correspondences for
GL_n, which was proved up to semisimplification by Harris-Taylor. More
precisely, for the n-dimensional l-adic representation R_l(\Pi) of the Galois
group of a CM-field L attached to a conjugate self-dual regular algebraic
cuspidal automorphic representation \Pi, which is square integrable at some
finite place, we show that Frobenius semisimplification of the restriction of
R_l(\Pi) to the decomposition group of a prime v of L not dividing l
corresponds to \Pi_v by the local Langlands correspondence. As a corollary, we
show the irreducibility of R_l(\Pi) when \Pi_v is square integrable for some
finite place v outside l. We also obtain conditional results in the case v|l.
