Crystalline Boundedness Principle
By A. Vasiu. 2002
63 citations recorded by the source corpus.
Abstract We prove that an F-crystal ( M , φ ) over an algebraically closed field k of characteristic p > 0 is determined by ( M , φ ) mod p n , where n ⩾ 1 depends only on the rank of M and on the greatest Hodge slope of ( M , φ ) . We also extend this result to triples ( M , φ , G ) , where G is a flat, closed subgroup scheme of GL M whose generic fibre is connected and has a Lie algebra normalized by φ. We get two purity results. If C is an F-crystal over a reduced F p -scheme S, then each stratum of the Newton polygon stratification of S defined by C , is an affine S-scheme (a weaker result was known before for S noetherian). The locally closed subscheme of the Mumford scheme A d , 1 , N k defined by the isomorphism class of a principally quasi-polarized p-divisible group over k of height 2d, is an affine A d , 1 , N k -scheme.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e9675fc578e1bf84669176fc2668072783462b66
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In Geometry and Topology
Citations in the corpus
- Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, methodology): “heme. Then every Ekedahl-Oort stratum Aw 0 (w∈ JW) is quasi-affine. 45 Proof. Let (A,ι,λ,η) be the restriction of the universal family over A0 to Aw 0 and let M= (M,C,D,ϕ0,ϕ1) be its attached D-zip. By [Va1] Theorem 5.3.1, we find a finite locally free surjective morphism g: S→ Aw 0 such that g∗Mis isom”
- The Newton stratification on deformations of local G-shtukas (2008, background): “By results of Vasiu [48], which were strengthened in [51], the Newton stratification is pure, that is the Newton polygon of a local G-shtuka over a connected scheme jumps in codimension one or is constant (Theorem 7.”