Time: 15:00-16:00, Monday, July 3 2023
Venue: E4-201, Yungu Campus
Host: Dr. Xing Gu, ITS
Speaker: Dr. Ningchuan Zhang, University of Pennsylvania
Title: Equivariant algebraic K-theory and special values of L-functions
Abstract:
The classical Quillen-Lichtenbaum Conjecture (QLC), proved by Voevodsky-Rost, connects algebraic K-theory of number fields with special values of their Dedekind zeta functions. In this talk, I will report my joint work in progress with Elden Elmanto to generalize this connection to L-functions associated to certain abelian characters of Galois groups of finite fields, function fields, and number fields.
On the K-theory side, we consider equivariant algebraic K-theory with coefficients in those abelian characters. On the number theory side, we express L-functions as alternating products of zeta functions. The key observation is that those alternating products are Euler numbers of certain spectral sequences to compute equivariant algebraic K-groups with coefficients in characters. We then prove the QLC for those L-functions by analyzing the spectral sequences above.
