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arXiv · 2103.12361

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

Fabrizio Andreatta
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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.

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Fabrizio Andreatta. 2021-03-23. On two mod p period maps: Ekedahl--Oort and fine Deligne--Lusztig stratifications. https://arxiv.org/abs/2103.12361

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