Turning non-smooth points into rational points

Abstract

In a recent paper, the author and Stöhr established a bound on the number of iterated Frobenius pullbacks needed to transform a non-smooth purely inseparable point on a regular geometrically integral curve into a rational point. In this paper we improve this result, by establishing a new bound that is sharp in every characteristic $p>0$.

arXiv comment13 pages. Final version. To appear in Indagationes Mathematicae