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2019 The Maillot–Rössler current and the polylogarithm on abelian schemes
Guido Kings, Danny Scarponi
Algebra Number Theory 13(2): 501-511 (2019). 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.

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Guido Kings. Danny Scarponi. "The Maillot–Rössler current and the polylogarithm on abelian schemes." Algebra Number Theory 13 (2) 501 - 511, 2019. https://doi.org/10.2140/ant.2019.13.501

Information

Received: 20 March 2018; Revised: 2 September 2018; Accepted: 10 November 2018; Published: 2019
First available in Project Euclid: 26 March 2019

zbMATH: 07042067
MathSciNet: MR3927054
Digital Object Identifier: 10.2140/ant.2019.13.501

Subjects:
Primary: 11G55
Secondary: 14G40

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

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2019
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