p-adic polylogarithms and p-adic Hecke L-functions for totally real fields

Abstract

The purpose of this article is to newly define the p-adic polylogarithm as an equivariant class in the cohomology of a certain infinite disjoint union of algebraic tori associated to a totally real field. We will then express the special values of p-adic L-functions interpolating nonpositive values of Hecke L-functions of the totally real field in terms of special values of these p-adic polylogarithms.

Canonical equivariant cohomology classes generating zeta values of totally real fields

“…The polylogarithms for general commutative group schemes were constructed by Huber-Kings [18]. Our discovery of the Shintani generating class arose from our attempt to explicitly describe various realizations of the Δ-equivariant version of the polylogarithm for the algebraic torus T. In subsequent research, we will explore the arithmetic implications of our insight (see for example [2]).…”