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BELYI˘ UNIFORMIZATION OF ELLIPTIC CURVES

Published online by Cambridge University Press:  01 July 1997

D. SINGERMAN  and
R. I. SYDDALL
D. SINGERMAN
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ
R. I. SYDDALL
Affiliation:
Department of Mathematics, University of Southampton, Southampton SO17 1BJ
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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.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 443 - 451
Copyright
© The London Mathematical Society 1997

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