On subruled function fields

Abstract

Let K be a function field with ground field k. A well known theorem of Jack Ohm proves that if k is infinite and K is separably subruled over k, then K is separably uniruled over k. At the end of his proof of this important result, Ohm asks if his theorem remains valid in the case of a finite ground field k. In this article we present an alternative proof of Ohm's theorem that is valid for all ground field k, finite or infinite, thereby answering Ohm's question.