Title: Shintani generating class and the p-adic polylogarithm for totally real fields
Speaker: 坂内健一 (Kenichi Bannai 慶應義塾/理研)
Time: 2020-5-27, 16:30 - 17:30
Place: Zoom;Registration(https://server.mcm.ac.cn/~zheng/SGA/Bannai)
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.