Finiteness of leaps in the sense of Hasse-Schmidt of unibranch curves in positive characteristic

Abstract

We prove that the set of leaps of the chain of m-integrable derivations of a curve X over a perfect field with geometrically unibranch singularities is finite. This result is a consequence of an affirmative answer to Seidenberg's question of extending, in positive characteristic, Hasse–Schmidt derivations of finite length of the local rings of X to their integral closures.