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.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246