##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Luciena Xiao

#### Caltech

## The Hecke Orbit Conjecture for PEL Type Shimura Varieties

##### Abstract:

Central leaves in the special fiber of Shimura varieties are the loci where the isomorphism class of the universal $p$-divisible group remains constant. The Hecke orbit conjecture asserts that every prime-to-$p$ Hecke orbit in a PEL type Shimura variety is dense in the central leaf containing it. This conjecture is proved for Hilbert modular varieties by C.-F. Yu, and for Siegel modular varieties by Chai and Oort. In this talk I give an overview of the conjecture and present my work that generalizes Chai and Oort's strategy to irreducible components of certain Newton strata on Shimura varieties of PEL type.

Host: Claus Sorensen

### March 12, 2020

### 2:00 PM

### AP&M 7321

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