A generalization of class field theory

In the late 1970's, a striking generalization of local class field theory was independently discovered by K. Kato and A. N. Parshin. These results were reformulated in 1992 by Y. Koya using the weight two motivic complex constructed by S. Lichtenbaum. In this talk, I will discuss some progress towards higher class field theory, and explain how, in Koya's setting of generalized class field theory, one can construct a Weil group. This seems to be a natural starting point for a variety of arithmetic applications.