##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Maria Fox

#### University of Oregon

## Supersingular Loci of Some Unitary Shimura Varieties

##### Abstract:

Unitary Shimura varieties are moduli spaces of abelian varieties with an action of a quadratic imaginary field, and extra structure. In this talk, we'll discuss specific examples of unitary Shimura varieties whose supersingular loci can be concretely described in terms of Deligne-Lusztig varieties. By Rapoport-Zink uniformization, much of the structure of these supersingular loci can be understood by studying an associated moduli space of p-divisible groups (a Rapoport-Zink space). We'll discuss the geometric structure of these associated Rapoport-Zink spaces as well as some techniques for studying them.

Host: Kiran Kedlaya

### May 6, 2021

### 2:00 PM

### Location: see https://www.math.ucsd.edu/\~{}nts/

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