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

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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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Acknowledgements

The authors express their sincere gratitude to the referee for carefully reading the manuscript and giving helpful suggestions. The authors would also like to thank the KiPAS program FY2014–2018 of the Faculty of Science and Technology at Keio University for providing an excellent environment making this research possible.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kouhoku-ku, Yokohama, 223-8522, Japan

    Kenichi Bannai, Kazuki Yamada & Shuji Yamamoto

  2. Mathematical Science Team, RIKEN Center for Advanced Intelligence Project )AIP), 1-4-1 Nihonbashi, Chuo-ku, Tokyo, 103-0027, Japan

    Kenichi Bannai, Kei Hagihara & Shuji Yamamoto

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  1. Kenichi Bannai
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  2. Kei Hagihara
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  3. Kazuki Yamada
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  4. Shuji Yamamoto
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Correspondence to Kenichi Bannai.

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This research was conducted as part of the KiPAS program FY2014–2018 of the Faculty of Science and Technology at Keio University. This research was supported in part by KAKENHI 26247004, 16J01911, 16K13742, 18H05233 as well as the JSPS Core-to-Core program “Foundation of a Global Research Cooperative Center in Mathematics focused on Number Theory and Geometry”

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Bannai, K., Hagihara, K., Yamada, K. et al. The Hodge realization of the polylogarithm on the product of multiplicative groups. Math. Z. 296, 1787–1817 (2020). https://doi.org/10.1007/s00209-020-02483-y

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  • DOI: https://doi.org/10.1007/s00209-020-02483-y

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