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Belyi Uniformization of Elliptic Curves
Author(s) -
Singerman D.,
Syddall R. I.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002834
Subject(s) - mathematics , elliptic curve , riemann surface , uniformization (probability theory) , genus , algebraic number field , uniformization theorem , riemann hypothesis , pure mathematics , supersingular elliptic curve , lattice (music) , geometric function theory , riemann–hurwitz formula , statistics , balance equation , botany , physics , markov model , markov chain , acoustics , biology
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. 1991 Mathematics Subject Classification 30F10, 11G05.