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

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the topic

Beijing-Paris-Tokyo arithmetic geometry webinar

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