The Hodge realization of the polylogarithm and the Shintani generating class for totally real fields

Kenichi Bannai, Hohto Bekki, Kei Hagihara, Tatsuya Ohshita, Kazuki Yamada, Shuji Yamamoto

研究成果: Article査読

抄録

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.

本文言語English
論文番号109716
ジャーナルAdvances in Mathematics
448
DOI
出版ステータスPublished - 2024 6月

ASJC Scopus subject areas

  • 数学一般

フィンガープリント

「The Hodge realization of the polylogarithm and the Shintani generating class for totally real fields」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル