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Purity of level m stratifications

By Adrian Vasiu and Torsten Wedhorn


Abstract. Let k be a field of characteristic p> 0. Let Dm be a BTm over k (i.e., an m-truncated Barsotti–Tate group over k). Let S be a k-scheme and let X be a BTm over S. Let SDm(X) be the subscheme of S which describes the locus where X is locally for the fppf topology isomorphic to Dm. If p ≥ 5, we show that SDm(X) is pure in S i.e., the immersion SDm(X) → S is affine. For p ∈ {2, 3}, we prove purity if Dm satisfies a certain property depending only on its p-torsion Dm[p]. For p ≥ 5, we apply the developed techniques to show that all level m stratifications associated to Shimura varieties of Hodge type are pure. Key words: truncated Barsotti–Tate groups, affine schemes, group actions

Topics: F-crystals, stratifications, purity, and Shimura varieties
Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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