An Eisenstein cocycle for imaginary quadratic fields

Abstract: I will give details of the general picture discussed by Nicolas Bergeron in the case of arithmetic subgroups of SL_N(k), where k is an imaginary quadratic field. I will introduce a cocycle for such groups whose values are polynomials in classical Kronecker—Eisenstein series. We will then see how this cocycle leads to explicit formulas for critical values of Hecke L—functions of degree N extensions of k, generalising work of Colmez. This is based on a work-in-progress with Pierre Charollois, Luis Garcia and Akshay Venkatesh.

Mathematics

Audience: researchers in the topic

CRM workshop: Arithmetic quotients of locally symmetric spaces and their cohomology

Series comments: Zoom registration: umontreal.zoom.us/meeting/register/tJwkfu6vpzItHtPb49yDLrPlCtLyb5kvjuYP