The Equivariant Polylogarithm and Eisenstein classes

Abstract: In this lecture, I will report on recent results, joint with Guido Kings, on the construction of equivariant Eisenstein classes. The equivariant polylogarithm is a very general tool for constructing motivic cohomology classes of arithmetic groups. A certain refinement of the de Rham realization of these classes gives interesting algebraic Eisenstein classes. As an application of our construction, we prove algebraicity results for critical Hecke L-values of totally imaginary fields. This generalizes previous results of Damerell, Shimura and Katz in the CM case. The integrality of our construction allows us to construct p-adic L-functions for totally imaginary fields at ordinary primes.

Mathematics

Audience: researchers in the topic

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

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