Belyi Uniformization of Elliptic Curves |
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Authors: | Singerman, D. Syddall, R. I. |
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Affiliation: | Department of Mathematics, University of Southampton Southampton SO17 1BJ |
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Abstract: | Belyi's Theorem implies that a Riemann surface X representsa curve defined over a number field if and only if it can beexpressed as U/, where U is simply-connected and is a subgroupof finite index in a triangle group. We consider the case whenX has genus 1, and ask for which curves and number fields canbe chosen to be a lattice. As an application, we give examplesof Galois actions on Grothendieck dessins. 1991 MathematicsSubject Classification 30F10, 11G05. |
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