5 - On the Base Change Problem:

Abstract

This chapter describes the generalization on the base change problem. The problem is connected with the class-field theory. A generalization of the construction of I and B to arbitrary extensions would constitute a non-abelian class field theory; it would imply that the Dedekind zeta function of a given number field of a certain degree over another field is the L-function attached to an automorphic form, or what amounts to the same, is a product of L-functions attached to automorphic cuspidal representations for various groups. It would also imply that every Artin-Hecke L-function is attached to an appropriate automorphic representation; in particular, it would imply Artin conjecture.