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BELYI˘ UNIFORMIZATION OF ELLIPTIC CURVES
Published online by Cambridge University Press: 01 July 1997
Abstract
Belyi˘'s Theorem implies that a Riemann surface X represents a curve defined over a number field if and only if it can be expressed as U/Γ, where U is simply-connected and Γ is a subgroup of finite index in a triangle group. We consider the case when X has genus 1, and ask for which curves and number fields Γ can be chosen to be a lattice. As an application, we give examples of Galois actions on Grothendieck dessins.
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- Research Article
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- © The London Mathematical Society 1997
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