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Liang Xiao : Goren-Oort stratification of Hilbert modular varieties

Posted by Majid Hadian-Jazi , part of the Number Theory Seminar.

At
March 19, 2013, 1 p.m.
In
SEO 636
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.