Caltech Home > PMA Home > Master Calendar > Number Theory Seminar
Thursday, October 10, 2019
4:00 PM - 6:00 PM
Linde Hall 387

# Number Theory Seminar

The Hecke Orbit Conjecture for PEL Type Shimura Varieties
Luciena Xiao, Mathematics Department, Caltech,

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.