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# Mathematics > Algebraic Geometry

# Title: The Hodge realization of the polylogarithm on the product of multiplicative groups

(Submitted on 12 Feb 2020)

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.

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