Purity Results on $F$-crystals

Abstract

For an $F^n$-crystal $\mathfrak{C}$ over a reduced locally Noetherian ${\mathbb{F}}_p$-scheme $S$, Vasiu first obtained the purity of the Newton polygon strata of $S$ defined by $\mathfrak{C}$. Deligne later obtained the purity of the $p$-rank strata of $S$ defined by $\mathfrak{C}$. We prove a stronger result that for every fixed point $P_0$ in the $xy$-coordinate plane, the reduced locally closed subscheme $S_{P_0}=\{s\in S| NP(\mathfrak C_s)\mbox{ has }P_0\mbox{ as a break point}\}$ of $S$ is pure in $S$ (A weaker result was known for the weak purity of $S_{p_0}$).

arXiv admin note: text overlap with arXiv:math/0205199 by other authors

References in corpus (1)

• An Improvement of de Jong-Oort's Purity Theorem