New Non-Abelian Zeta Functions

L. Weng

Abstract

In this talk, we use stability to introduce new non-abelian zeta functions for number fields, based on a new arithmetic cohomology, as natural generalizations of Dedekind zeta functions (along the line of Iwasawa and Tate). Related work for function fields will also be discussed. Just as in class field theory, we expect that these new non-abelian zeta functions would play a key role in non-abelian CFT.