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Bannai, Kenichi [Author] ; Abbes, Ahmed (Organization) [Other]; Hu, Yongquan (Organization) [Other]; Orgogozo, Fabrice (Organization) [Other]; Saito, Takeshi (Organization) [Other]; Shiho, Atsushi (Organization) [Other]; Tian, Ye (Organization) [Other]; Tsuji, Takeshi (Organization) [Other]; Zheng, Weizhe (Organization) [Other]; Hagihara, Kei [Other]; Yamada, Kazuki [Other]; Yamamoto, Shuji [Other]

Shintani generating class and the p-adic polylogarithm for totally real fields

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  • Media type: E-Book; Video
  • Title: Shintani generating class and the p-adic polylogarithm for totally real fields
  • Contributor: Bannai, Kenichi [Author]; Abbes, Ahmed (Organization) [Other]; Hu, Yongquan (Organization) [Other]; Orgogozo, Fabrice (Organization) [Other]; Saito, Takeshi (Organization) [Other]; Shiho, Atsushi (Organization) [Other]; Tian, Ye (Organization) [Other]; Tsuji, Takeshi (Organization) [Other]; Zheng, Weizhe (Organization) [Other]; Hagihara, Kei [Other]; Yamada, Kazuki [Other]; Yamamoto, Shuji [Other]
  • Published: [Erscheinungsort nicht ermittelbar]: Institut des Hautes Études Scientifiques (IHÉS), 2020
  • Published in: Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo ; (Jan. 2020)
  • Extent: 1 Online-Ressource (172 MB, 01:02:40:02)
  • Language: English
  • DOI: 10.5446/54700
  • Identifier:
  • Origination:
  • Footnote: Audiovisuelles Material
  • Description: In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke L-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke L-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto
  • Access State: Open Access
  • Rights information: Attribution - Non Commercial (CC BY-NC)