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Institute for the Physics and Mathematics of the UniverseWPI

IPMU Math seminar in Kashiwa

Date: June 12, 2008, 15:30 - 17:00
Place: IPMU Prefab-B, Kashiwa Campus of the University of Tokyo
Speaker: Shushi Harashita (IPMU)
Title: Generic Newton polygons of Ekedahl-Oort strata in the moduli space of abelian varieties.
Abstract: We study the moduli space of principally polarized abelian varieties in positive characteristic. The moduli space has two main stratifications, called Newton polygon (NP) stratification and Ekedahl-Oort (EO) stratification. It is considered very important in arithmetic geometry to clarify the singularities of NP strata. As a first step it would be natural to investigate the intersections of NP strata and EO strata. In this talk I will introduce an algorithm determining the Newton polygon of any generic point of each EO stratum, which is closely related to Oort's conjecture on the intersections of NP strata and EO strata. I will also show that certain unions of EO strata contained in the supersingular locus can be beautifully described in terms of Deligne-Lusztig varieties.