Higher analytic torsion, polylogarithms and norm compatible elements on abelian schemes

TL;DR

This paper links the degree 0 polylogarithm on abelian schemes to higher analytic torsion forms, providing an axiomatic framework and a cohomological description involving the Poincaré bundle.

Contribution

It introduces a simple axiomatic approach to the degree 0 polylogarithm on abelian schemes and relates its analytic realization to Bismut-Köhler torsion forms.

Findings

Axiomatic description of the degree 0 polylogarithm

Connection between polylogarithm and higher analytic torsion forms

Description of the cohomological realization involving the Poincaré bundle

Abstract

We give a simple axiomatic description of the degree 0 part of the polylogarithm on abelian schemes and show that its realisation in analytic Deligne cohomology can be described in terms of the Bismut-K\"ohler higher analytic torsion form of the Poincar\'e bundle.