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Explore the relationship between two fundamental mod p period maps in algebraic geometry through this mathematical lecture by Fabrizio Andreatta from the University of Milan. Examine Shimura varieties of Hodge type with smooth integral models at odd primes p > 3, focusing on their perfectoid covers and the Hodge-Tate period map developed by Caraiani and Scholze. Compare the pull-backs of the Ekedahl-Oort stratification on the mod p special fiber with the fine Deligne-Lusztig stratification on the flag variety target of the Hodge-Tate period map. Discover applications to proving non-emptiness results for Ekedahl-Oort strata, connecting advanced concepts in arithmetic geometry, perfectoid geometry, and the theory of Shimura varieties.
