Westlake Math Colloquium第四十期 | Ningchuan Zhang: Equivariant algebraic K-theory and special values of L-functions

2023-06-28 15:25:18



主持人:理论科学研究院 古星博士

主讲人: 宾夕法尼亚大学 张凝川博士

讲座主题Equivariant algebraic K-theory and special values of L-functions


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.