  We reprove the Local Langlands Correspondence for $\GL_n$ over $p$-adic
fields as well as the existence of $\ell$-adic Galois representations attached
to (most) regular algebraic conjugate self-dual cuspidal automorphic
representations, for which we prove a local-global compatibility statement as
in the book of Harris-Taylor.
  In contrast to the proofs of the Local Langlands Correspondence given by
Henniart and Harris-Taylor our proof completely by-passes the numerical Local
Langlands Correspondence of Henniart. Instead, we make use of a previous result
describing the inertia-invariant nearby cycles in certain regular situations.
