Purity of G-zips

2012/10/31 by Yaroslav Yatsyshyn, Yatsyshyn, Yaroslav
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1210.8396

openalex publication_date 2012/10/31 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field of characteristic p>0, and S an scheme over k. An F-zip is basically a locally free O_S-module of finite rank endowed with two filtration and an Frobenius-linear isomorphism between their graded pieces. The natural generalization of this notion for a reductive algebraic group G/k is an "F-zip with G-structure", a so-called G-zip introduced by R. Pink, T. Wedhorn, P. Ziegler. A G-zip I over S yields the stratification of the base scheme in loci, where I has locally a constant isomorphism class for the fppf topology. We show that these strata are affine and give a number of geometric applications of this purity result.

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• Discrete invariants of varieties in positive characteristic
• Purity of level m stratifications
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