The realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne-Beilinson cohomology

TL;DR

This paper demonstrates how to realize the degree zero part of the motivic polylogarithm on abelian schemes within Deligne-Beilinson cohomology using Burgos' theory of arithmetic Chow groups.

Contribution

It introduces a novel method to realize the degree zero motivic polylogarithm in Deligne-Beilinson cohomology leveraging Burgos' arithmetic Chow groups.

Findings

Realization of the degree zero polylogarithm in Deligne-Beilinson cohomology.

Application of Burgos' theory to motivic polylogarithms.

Advancement in understanding the cohomological aspects of abelian schemes.

Abstract

We use Burgos theory of arithmetic Chow groups to exhibit a realization of the degree zero part of the polylogarithm on abelian schemes in Deligne-Beilinson cohomology.