Title: Analogs of Dirichlet L-functions in chromatic homotopy theory
Speaker: Ningchuan Zhang
Speaker Info: UIUC
The relation between Eisenstein series and the J-homomorphism is an important topic in chromatic homotopy theory at height 1. Both sides are related to the special values of the Riemann ζ-function. This relation is most clearly understood in the context of elliptic cohomology and topological modular forms.Date: Monday, October 21, 2019
Number theorists have studied the twistings of the Riemann ζ-functions and Eisenstein series by Dirichlet characters. Motivated by the Dirichlet equivariance of these twisted Eisenstein series, we introduce the Dirichlet J-spectra in this talk. The homotopy groups of these Dirichlet J-spectra are related to the special values of the Dirichlet L-functions, and thus to congruences of the twisted Eisenstein series. If time allows, we will also explain the connection between Dirichlet J-spectra and the twisted Eisenstein series by generalizing Katz's algebro-geometric explanation of congruences of the (untwisted) Eisenstein series.