Purity of G-zips

Yaroslav Yatsyshyn

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arXiv · 1210.8396

Purity of G-zips

Yaroslav Yatsyshyn

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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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BibTeX RIS

Yaroslav Yatsyshyn. 2014-05-14. Purity of G-zips. https://arxiv.org/abs/1210.8396

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