On the geometric connected components of local Shimura varieties

Abstract: Through the recent introduction of the theory of diamonds, P. Scholze was able to define local versions of Shimura varieties. These are rigid-analytic spaces that generalize the generic fiber of a Rapoport-Zink space. It is widely expected that the cohomology of these interesting spaces realizes instances of the Langlands correspondence. In this talk we describe the geometric connected components of these moduli spaces and relate it to local class field theory.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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