The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle

Sprang, Johannes

doi:10.2140/ant.2020.14.551

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The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle

Johannes Sprang

Vol. 14 (2020), No. 3, 545–585

DOI: 10.2140/ant.2020.14.551

Abstract

We describe the algebraic de Rham realization of the elliptic polylogarithm for arbitrary families of elliptic curves in terms of the Poincaré bundle. Our work builds on previous work of Scheider and generalizes results of Bannai, Kobayashi and Tsuji, and Scheider. As an application, we compute the de Rham–Eisenstein classes explicitly in terms of certain algebraic Eisenstein series.

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Keywords

de Rham cohomology, polylogarithm, Eisenstein classes

Mathematical Subject Classification 2010

Primary: 11G55

Secondary: 14H52

Milestones

Received: 26 February 2018

Revised: 25 June 2019

Accepted: 8 November 2019

Published: 1 June 2020

Authors

Johannes Sprang
Fakultät für Mathematik Universität Regensburg Germany

Vol. 14, No. 3, 2020