Belyi's theoerm in characteristic two

Abstract

We prove an analogue of Belyi's theorem in characteristic two. Our proof consists of the following three steps. We first introduce a new notion called "pseudo-tame" for morphisms between curves over an algebraically closed field of characteristic two. Secondly, we prove the existence of a "pseudo-tame" rational function by proving vanishing of an obstruction class. Finally we will construct a tamely ramified rational function from the "pseudo-tame" rational function.