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Title: On two mod p period maps: Ekedahl-Oort and fine Deligne-Lusztig stratifications
Consider the integral model S of a Shimura variety with good reduction, in mixed characteristic 0-p. Caraiani and Scholze construct a perfectoid cover of the generic fiber of S and the so called Hodge-Tate period map, with target a suitable flag variety. In this talk I will compare the pull-back to this perfectoid cover of two stratifications. The first is the Ekedhal-Oort stratification on the mod p special fiber of S. The second is the fine Deligne-Lusztig stratification on the mod p special fiber of the flag variety.