On the local Langlands correspondence for unitary groups in positive characteristic

We present a proof of the existence of a Base Change map from generic representations of U(N) to generic representations of GL(N). The local lift is uniquely characterized by the fact that it preserves local L-functions and root numbers, by a result of Henniart. The proof uses global and local methods of automorphic forms and the representation theory of p-adic groups. The necessary L-functions are provided by the Langlands-Shahidi method over function fields.