Belyi's theorem revisited

TL;DR

This paper presents a straightforward proof of Belyi's theorem, providing an explicit degree bound for the defining number field of Belyi surfaces, enhancing understanding of their algebraic properties.

Contribution

It offers an elementary, self-contained proof of Belyi's theorem along with explicit bounds on the degree of the defining number field.

Findings

Elementary proof of Belyi's theorem

Explicit bound for the degree of the defining number field

Simplifies understanding of Belyi surfaces

Abstract

We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.