拓扑研讨班：Equivariant algebraic K-theory and L-functions of Galois representations

中科院数学与系统科学研究院

数学研究所

学术报告

拓扑研讨班

报告人：张凝川（Indiana University Bloomington）

题  目：Equivariant algebraic K-theory and L-functions of Galois representations

时  间：2023.12.27（星期三）10:00-11:00

地  点：数学院南楼N933

摘  要：The profound connection between the algebraic K-theory and zeta functions was first hinted in two classical results in algebraic number theory: Dirichlet’s unit theorem and the class number formula. Those results were later generalized to Borel’s theorem on ranks of algebraic K-groups of number fields and the celebrated Quillen-Lichtenbaum Conjecture (QLC), proved by Voevodsky and Rost.

In this talk, I will explain how to generalize the QLC to L-functions associated to Galois representations of finite, function, and number fields. On the K-theory side, we twist equivariant algebraic K-theory with equivariant Moore spectra associated to Galois representations. Those equivariant algebraic K-groups with coefficients in Galois representations are then computed by an equivariant Atiyah-Hirzebruch spectral sequence. This is joint work in progress with Elden Elmanto.