Algebra & Number Theory

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

Johannes Sprang

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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.

Article information

Source
Algebra Number Theory, Volume 14, Number 3 (2020), 545-585.

Dates
Received: 26 February 2018
Revised: 25 June 2019
Accepted: 8 November 2019
First available in Project Euclid: 2 July 2020

Permanent link to this document
https://projecteuclid.org/euclid.ant/1593655265

Digital Object Identifier
doi:10.2140/ant.2020.14.545

Mathematical Reviews number (MathSciNet)
MR4113775

Subjects
Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx]

Keywords
de Rham cohomology polylogarithm Eisenstein classes

Citation

Sprang, Johannes. The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle. Algebra Number Theory 14 (2020), no. 3, 545--585. doi:10.2140/ant.2020.14.545. https://projecteuclid.org/euclid.ant/1593655265


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