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تسجيل مستخدم جديدPurity of Crystalline Strata
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Let $p$ be a prime. Let $ninmathbb N-{0}$. Let $mathcal C$ be an $F^n$-crystal over a locally noetherian $mathbb F_p$-scheme $S$. Let $(a,b)inmathbb N^2$. We show that the reduced locally closed subscheme of $S$ whose points are exactly those $xin S$ such that $(a,b)$ is a break point of the Newton polygon of the fiber $mathcal C_x$ of $mathcal C$ at $x$ is pure in $S$, i.e., it is an affine $S$-scheme. This result refines and reobtains previous results of de Jong--Oort, Vasiu, and Yang. As an application, we show that for all $min mathbb N$ the reduced locally closed subscheme of $S$ whose points are exactly those $xin S$ for which the $p$-rank of $mathcal C_x$ is $m$ is pure in $S$; the case $n=1$ was previously obtained by Deligne (unpublished) and the general case $nge 1$ refines and reobtains a result of Zink.
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