On two mod p period maps: Ekedahl–Oort and fine Deligne–Lusztig stratifications
AbstractConsider a Shimura variety of Hodge type admitting a smooth integral model S at an odd prime $$p\ge 5$$ p ≥ 5 . Consider its perfectoid cover $$S^{\text {ad}}(p^\infty )$$ S ad ( p ∞ ) and the Hodge–Tate period map introduced by Caraiani and Scholze. We compare the pull-back to $$S^{\text {ad}}(p^\infty )$$ S ad ( p ∞ ) of the Ekedahl–Oort stratification on the mod p special fiber of a toroidal compactification of S and the pull back to $$S^\text {ad}(p^\infty )$$ S ad ( p ∞ ) 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.
2018 ◽
Vol 70
(2)
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pp. 451-480
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Keyword(s):
2015 ◽
Vol 16
(5)
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pp. 899-945
2021 ◽
Vol 90
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pp. 108824