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arXiv · 1803.00833

The Maillot-Rössler current and the polylogarithm on abelian schemes

Guido Kings·Danny Scarponi
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Abstract

We give a conceptual proof of the fact that the realisation 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. 2018-03-02. The Maillot-Rössler current and the polylogarithm on abelian schemes. https://doi.org/10.2140/ant.2019.13.501

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