The Hodge realization of the polylogarithm on the product of multiplicative groups

Abstract

The purpose of this article is to describe explicitly the polylogarithm class in absolute Hodge cohomology of a product of multiplicative groups, in terms of the Bloch-Wigner-Ramakrishnan polylogarithm functions. We will use the logarithmic Dolbeault complex defined by Burgos to calculate the corresponding absolute Hodge cohomology groups.

arXiv comment28 pages

References in corpus (2)

• On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves
• Polylogarithm for families of commutative group schemes

Cited by in corpus (1)

• The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields