2002/05/31 by Adrian Vasiu · 3 citations
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG #math.NT #msc:11G10 #msc:11G18 #msc:14F30 #msc:14G35 #msc:20G25
paper · pdf · doi:10.1016/j.ansens.2005.12.003
published as Ann. Scient. Éc. Norm. Sup. 39 (2006), no. 2, pp. 245--300 · Final version (63 pages) accepted for publication in Ann. Sci. Ec. Norm. Sup
arxiv created 2006/01/04 · openalex publication_date 2006/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 2 d , is an affine A d , 1 , N k -scheme.