On two mod p period maps: Ekedahl--Oort and fine Deligne--Lusztig stratifications

DOI10.1007/S00208-021-02356-7arXiv2103.12361MaRDI QIDQ6363497

Publication date: 23 March 2021

Abstract: Consider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime p>3. Consider its perfectoid cover S(p^infty) and the Hodge-Tate period map introduced by A. Caraiani and P. Scholze. We compare the pull-back to S(p^infty) of the Ekedahl-Oort stratification on the mod p special fiber of S and the pull back to S(p^infty) of the fine Deligne-Lusztig stratification on the mod p special fiber of the flag variety which is the target of the Hodge-Tate period map. An application to the non-emptiness of Ekedhal-Oort strata is provided.

Mathematics Subject Classification ID

Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

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