Algebra/Topology seminar -- Elden Elmanto (CANCELLED)

Speaker: Elden Elmanto

Title: Categorical geometric class field theory

Class field theory is the study of abelian extensions of global and local fields via some kind of reciprocity law. It can be viewed as the abelian, simplest case of Langlands reciprocity. While recent progress has focused on the geometric, categorical Langlands program occurring over curves, it is natural to ask for geometric, categorical versions of class field theory occurring over surfaces. We offer a conjectural picture in the Betti and étale case using the moduli stack of zero cycles built out of non-A^1-invariant motivic cohomology. This picture categorifies some work of Kato and Saito on the 80s in the case of finite fields. All of this is joint work, very much in progress, with Nick Rozenblyum.