Algebraic curves uniformized by congruence subgroups of triangle groups

John Voight; Pete L. Clark

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Algebraic curves uniformized by congruence subgroups of triangle groups

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arxiv 1506.01371 v1 pith:K5AEQEKC submitted 2015-06-03 math.NT

Algebraic curves uniformized by congruence subgroups of triangle groups

Pete L. Clark , John Voight This is my paper

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keywords groupssubgroupstrianglecongruencecurvesassociatedalgebraicarithmetic

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We construct certain subgroups of hyperbolic triangle groups which we call "congruence" subgroups. These groups include the classical congruence subgroups of SL_2(ZZ), Hecke triangle groups, and 19 families of arithmetic triangle groups associated to Shimura curves. We determine the field of moduli of the curves associated to these groups and thereby realize the groups PSL_2(q) and PGL_2(q) regularly as Galois groups.

Algebraic curves uniformized by congruence subgroups of triangle groups

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