时间：2020年5月27日（周三）16:30—17:30（Zoom网络研讨会，请提前<a href="https://server.mcm.ac.cn/~zheng/SGA/Bannai">注册</a>）
报告人：坂内健一（Kenichi Bannai　慶應義塾/理研）
题目：Shintani generating class and the p-adic polylogarithm for totally real fields
摘要：
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.