The Maillot–Rössler current and the polylogarithm on abelian schemes

Kings, Guido; Scarponi, Danny

doi:10.2140/ant.2019.13.501

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The Maillot–Rössler current and the polylogarithm on abelian schemes

Guido Kings and Danny Scarponi

Vol. 13 (2019), No. 2, 501–511

DOI: 10.2140/ant.2019.13.501

Abstract

We give a structural proof of the fact that the realization of the degree-zero part of the polylogarithm on abelian schemes in analytic Deligne cohomology can be described in terms of the Bismut–Köhler higher analytic torsion form of the Poincaré bundle. Furthermore, we provide a new axiomatic characterization of the arithmetic Chern character of the Poincaré bundle using only invariance properties under isogenies. For this we obtain a decomposition result for the arithmetic Chow group of independent interest.

Keywords

abelian polylogarithm, arithmetic Chow groups, Arakelov geometry, Deligne cohomology

Mathematical Subject Classification 2010

Primary: 11G55

Secondary: 14G40

Milestones

Received: 20 March 2018

Revised: 2 September 2018

Accepted: 10 November 2018

Published: 2 March 2019

Authors

Guido Kings
Fakultät für Mathematik Universität Regensburg Regensburg Germany

Danny Scarponi
King’s College London London United Kingdom

Vol. 13, No. 2, 2019