Number Theory Seminar
Liang Xiao
University of Chicago
Goren-Oort stratification of Hilbert modular varieties
Abstract: The special fiber of a modular curve admits a stratification by the
ordinary locus and the supersingular locus, where the latter is given
by the zero locus of the Hasse invariant. Goren and Oort generalized
this picture to define a stratification of the special fiber of
Hilbert modular varieties, given by the zero locus of partial Hasse
invariants. I will discuss the geometric structure of this
stratification and various applications of the structure theorem. If
time permits, I will explain certain (mostly conjectural)
generalizations of the construction to PEL type Shimura varieties.
This is an ongoing joint project with David Helm and Yichao Tian.
Tuesday March 19, 2013 at 1:00 PM in SEO 636