On the geometric connected components of unramified local Shimura varieties

Abstract: Through the recent theory of diamonds, P. Scholze constructs local Shimura varieties attached to any reductive group. These are rigid-analytic spaces that generalize the generic fiber of a Rapoport–Zink space. It is widely expected that these interesting spaces realize in their cohomology instances of the local Langlands correspondence. In this talk, we describe the set of connected components of unramified local Shimura varieties (more generally moduli spaces of mixed characteristic shtukas), and describe the relation to local class field theory.

number theoryrepresentation theory

Audience: researchers in the discipline

The 2020 Paul J. Sally, Jr. Midwest Representation Theory Conference

Series comments: The 44th Midwest Representation Theory Conference will address recent progress in the theory of representations for groups over non-archimedean local fields, and connections of this theory to other areas within mathematics, notably number theory and geometry.

In order to receive information on how to participate (to be sent out closer to the conference), please register by October 14 here: forms.gle/zFAnQBnuPGRnKzMr7