Purity of crystalline strata

IF 0.8 Q2 MATHEMATICS
Jinghao Li, A. Vasiu
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引用次数: 0

Abstract

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S$ for which the $p$-rank of $\mathcal C_x$ is $m$ is pure in $S$; the case $n=1$ was previously obtained by Deligne (unpublished) and the general case $n\ge 1$ refines and reobtains a result of Zink.
结晶地层的纯度
让$p$是素数。设$n\in\mathbb n-\{0\}$。设$\mathcal C$是局部noetherian$\mathbb F_p$-方案$S$上的$F^n$-晶体。设$(a,b)\in\mathbb N^2$。我们证明了点正是S$中的$x\,使得$(a,b)$是$\mathcal C$的纤维$\mathcalC_x$在$x$处的牛顿多边形的断点的$S$的约化局部闭子方案在$S$中是纯的,即它是仿射$S$-方案。这一结果对德容、瓦修和杨以前的研究结果进行了改进和重新诠释。作为一个应用,我们证明了对于所有$m\in\mathbb N$,其点正是S$中的$x\的$p$-mathcal C_x$的秩为$m$的$S$的降局部闭子血红素在$S$中是纯的;案例$n=1$先前由Deligne获得(未发表),一般案例$n\ge1$改进并重新获得Zink的结果。
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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