An Improvement of de Jong-Oort's Purity Theorem

Consider an $F$-crystal over a noetherian scheme $S$. De Jong–Oort’s purity theorem states that the associated Newton polygons over all points of $S$ are constant if this is true outside a subset of codimension bigger than 1. In this paper we show an improvement of the theorem, which says that the Newton polygons over all points of $S$ have a common break point if this is true outside a subset of codimension bigger than 1.