The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929402955169792 |
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| author | Bannai, Kenichi Bekki, Hohto Hagihara, Kei Ohshita, Tatsuya Yamada, Kazuki Yamamoto, Shuji |
| author_facet | Bannai, Kenichi Bekki, Hohto Hagihara, Kei Ohshita, Tatsuya Yamada, Kazuki Yamamoto, Shuji |
| contents | In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_03285 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields Bannai, Kenichi Bekki, Hohto Hagihara, Kei Ohshita, Tatsuya Yamada, Kazuki Yamamoto, Shuji Number Theory Algebraic Geometry 14C30, 11G55 In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields. |
| title | The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields |
| topic | Number Theory Algebraic Geometry 14C30, 11G55 |
| url | https://arxiv.org/abs/2207.03285 |