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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Algebraic curves uniformized by congruence subgroups of triangle groups
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by Pete L. Clark and John Voight PDF
Trans. Amer. Math. Soc. 371 (2019), 33-82 Request permission


We construct certain subgroups of hyperbolic triangle groups which we call “congruence” subgroups. These groups include the classical congruence subgroups of $\mathrm {SL}_2(\mathbb {Z})$, 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 $\mathrm {PSL}_2(\mathbb {F}_q)$ and $\mathrm {PGL}_2(\mathbb {F}_q)$ regularly as Galois groups.
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Additional Information
  • Pete L. Clark
  • Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
  • MR Author ID: 767639
  • Email:
  • John Voight
  • Affiliation: Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, Vermont 05401 – and – Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755
  • MR Author ID: 727424
  • ORCID: 0000-0001-7494-8732
  • Email:
  • Received by editor(s): September 12, 2016
  • Received by editor(s) in revised form: November 22, 2016
  • Published electronically: July 20, 2018
  • Additional Notes: The second author was supported by an NSF CAREER Award (DMS-1151047).
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 33-82
  • MSC (2010): Primary 11F06
  • DOI:
  • MathSciNet review: 3885137