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The Hodge realization of the polylogarithm on the product of multiplicative groups. (English) Zbl 1469.11223

Summary: 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.

MSC:

11G55 Polylogarithms and relations with \(K\)-theory
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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References:

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