2003/06/24 by B.J. Moonen, B. Moonen, Moonen, B. +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #11G18 #14F40 (Primary) 14J28 #14J10 #14K10 #20G40 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Plant and Fungal Species Descriptions #math.AG #math.NT #msc:11G18 #msc:14F40 #msc:14J10 #msc:14J28 #msc:14K10 #msc:20G40
paper · pdf · doi:10.48550/arxiv.math/0306339
35 pages, minor changes in exposition, major changes to introduction
openalex publication_date 2003/06/24 · arxiv created 2004/04/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If S is a scheme of characteristic p, we define an F-zip over S to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism X→ S satisfying certain conditions the de Rham bundles Hn\rm dR(X/S) have a natural structure of an F-zip. We give a complete classification of F-zips over an algebraically closed field by studying a semi-linear variant of a variety that appears in recent work of Lusztig. For every F-zip over S our methods give a scheme-theoretic stratification of S. If the F-zip is associated to an abelian scheme over S the underlying topological stratification is the Ekedahl-Oort stratification. We conclude the paper with a discussion of several examples such as good reductions of Shimura varieties of PEL type and K3-surfaces.