Singularities in the Ekedahl-Oort stratification
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M7-411
The moduli space of abelian varieties in positive characteristic admits several interesting stratifications. In this talk, we examine the Ekedahl-Oort stratification, defined in terms of isomorphism classes of the p-torsion. We give a criterion for the normality of the Zariski closure of a stratum (or a subset thereof). More generally, this theory applies to all Hodge-type Shimura varieties, attached to more general reductive groups. As an example, we give a complete characterization for the smoothness of one-dimensional strata. Moreover, our method makes it possible to construct Hasse invariants whose vanishing locus is reduced, which is an important technical tool in the study of p-adic modular forms. This talk is based on joint work with Lorenzo La Porta (Genoa) and Stefan Reppen (Berkeley).