Belyi's theoerm in characteristic two
Number Theory
2020-02-19 v2 Algebraic Geometry
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.
Cite
@article{arxiv.1708.03036,
title = {Belyi's theoerm in characteristic two},
author = {Yusuke Sugiyama and Seidai Yasuda},
journal= {arXiv preprint arXiv:1708.03036},
year = {2020}
}