Vol. 13, No. 2, 2019

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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

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.

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abelian polylogarithm, arithmetic Chow groups, Arakelov geometry, Deligne cohomology
Mathematical Subject Classification 2010
Primary: 11G55
Secondary: 14G40
Received: 20 March 2018
Revised: 2 September 2018
Accepted: 10 November 2018
Published: 2 March 2019
Guido Kings
Fakultät für Mathematik
Universität Regensburg
Danny Scarponi
King’s College London
United Kingdom