University of California, Santa Cruz
When
2 – 3 p.m., Jan. 21, 2025
Where
Title: Strata intersections in some unitary Shimura varieties
Abstract: Unitary Shimura varieties are moduli spaces of abelian varieties with a certain extra structure, including a signature condition. An effective way to understand these spaces in positive characteristic is by stratifying them, of which two are of interest: the Ekedah-Oort (EO) stratification, defined using the p-torsion group scheme structure up to isomorphism, and the Newton stratification, defined using the p-divisible group structure up to isogeny. We will see in several concrete examples that these two stratifications are very different, reflecting that these two invariants capture very different attributes of the abelian varieties. In joint work with E. Anne, M. Fox, H. Goodson, S. Groen, and S. Nair, we take a specific stratum in the Newton stratification - the supersingular stratum - and study its intersection with the EO stratification in some low signature cases.