Belyi's theorem revisited

2001/08/31 by Bernhard Köck, Köck, Bernhard
Computer Science · Mathematics · #12F10 #14H25 #14H30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0108222

openalex publication_date 2001/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the Belyi degree of a number field
• Bounding the Degree of Belyi Polynomials
• The Belyi degree is computable
• On the Belyi degree(s) of a curve defined over a number field
• Geometry of division rings