arXiv subjects

Yaroslav Yatsyshyn

Publications and source records attributed to Yaroslav Yatsyshyn.

2 recordsLinked to original sources

arXiv2016

Purity of Zip Strata with Applications to Ekedahl-Oort Strata of Shimura Varieties of Hodge Type

We show that the zip stratification given by an arbitrary $\Ghat$-zip over a scheme is pure. We deduce purity of the level-$m$-stratification for truncated Barsotti-Tate groups and purity of the Ekedahl-Oort stratification for special fibers of good models of Shimura varieties of Hodge type. We also show that all Ekedahl-Oort strata are quasi-affine schemes and generalize several properties of the Bruhat stratification from the PEL case to the case of Shimura varieties of Hodge type.

math.AG↗

arXiv2014

Purity of G-zips

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.

math.AG↗