Crystalline boundedness principle

dc.creatorVasiu, Adrian
dc.date2002-05-17
dc.date2006-01-04
dc.date.accessioned2026-07-07T06:35:29Z
dc.date.available2026-07-07T06:35:29Z
dc.descriptionWe prove that an $F$-crystal $(M,\vph)$ over an algebraically closed field $k$ of characteristic $p>0$ is determined by $(M,\vph)$ mod $p^n$, where $n\ge 1$ depends only on the rank of $M$ and on the greatest Hodge slope of $(M,\vph)$. We also extend this result to triples $(M,\vph,G)$, where $G$ is a flat, closed subgroup scheme of ${\bf GL}_M$ whose generic fibre is connected and has a Lie algebra normalized by $\vph$. We get two purity results. If ${\got C}$ is an $F$-crystal over a reduced ${\bf F}_p$-scheme $S$, then each stratum of the Newton polygon stratification of $S$ defined by ${\got C}$, is an affine $S$-scheme (a weaker result was known before for $S$ noetherian). The locally closed subscheme of the Mumford scheme ${\Ma_{d,1,N}}_k$ defined by the isomorphism class of a principally quasi-polarized $p$-divisible group over $k$ of height 2d, is an affine ${\Ma_{d,1,N}}_k$-scheme.
dc.descriptionFinal version (63 pages) accepted for publication in Ann. Sci. Ec. Norm. Sup
dc.identifierhttps://arxiv.org/abs/math/0205199
dc.identifierhttp://arxiv.org/abs/math/0205199
dc.identifierAnn. Scient. Éc. Norm. Sup. 39 (2006), no. 2, pp. 245--300
dc.identifierdoi:10.1016/j.ansens.2005.12.003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99809
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.subject11G10, 11G18, 14F30, 14G35, and 20G25
dc.titleCrystalline boundedness principle
dc.typetext

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