结晶层的纯度
Purity of Crystalline Strata
摘要：
让$p$是一个素数。设$n\in\mathbb N-\{0\}$。设$\mathcal C$是局部Noether $\mathbb F_p$ -方案$S$上的$F^n$ -晶体.让$(a,b)\in\mathbb N^2$。证明了$S$的约化局部闭子概型在$S$中是纯的，其点恰好是使得$(a,b)$是$\mathcal C$的纤维$\mathcal C_x$在$x$处的牛顿多边形的断点的那些$x\in S$，即，它是一个仿射$S$格式。这一结果改进并重新获得了de Jong-Oort，Vasiu和Yang的先前结果。作为一个应用程序，我们表明，对于所有的$m\in \mathbb N$的减少局部封闭的子计划的$S$的点正是那些$x\in S$的$p$ -秩的$\mathcal C_x$是$m$是纯的$S$ ; $n=1$的情况下，以前获得的Deligne（未发表）和一般情况下$n\ge 1$细化和reobtained结果的Zink。
英文摘要：
Let $p$ be a prime. Let $n\in\mathbb N-\{0\}$. Let $\mathcal C$ be an $F^n$-crystal over a locally noetherian $\mathbb F_p$-scheme $S$. Let $(a,b)\in\mathbb N^2$. We show that the reduced locally closed subscheme of $S$ whose points are exactly those $x\in S$ 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 $m\in \mathbb N$ the reduced locally closed subscheme of $S$ whose points are exactly those $x\in S$ for which the $p$-rank of $\mathcal C_x$ is $m$ is pure in $S$; the case $n=1$ was previously obtained by Deligne (unpublished) and the general case $n\ge 1$ refines and reobtains a result of Zink.
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