Purity of crystalline strata

Given an $F$-crystal $C$ over a scheme $S$ of positive characteristic $p$, one can associate many reduced locally closed subschemes $T$ of $S$ defined by the property that a suitable invariant of $F$-crystals is constant on the fibres of $C$ over points of $S$. A basic problem is to study different properties of such locally closed subschemes $T$.

In this talk, we present a survey of purity results for locally closed subschemes $T$ of $S$, including some of them which were obtained by us and by the graduate student Jinghao Li.