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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A finiteness property of abelian varieties with potentially ordinary good reduction
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by Haruzo Hida PDF
J. Amer. Math. Soc. 25 (2012), 813-826 Request permission


For a prime $p>2$, contrary to super-singular cases, we prove that there are only finitely many twist equivalence classes of non-CM $\mathbb {Q}$-simple abelian varieties of $GL(2)$-type with potentially ordinary reduction modulo $p$ and good reduction everywhere outside $p$.
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Additional Information
  • Haruzo Hida
  • Affiliation: Department of Mathematics, UCLA, Los Angeles, California 90095-1555
  • MR Author ID: 213427
  • Email:
  • Received by editor(s): May 24, 2011
  • Received by editor(s) in revised form: December 3, 2011
  • Published electronically: January 25, 2012
  • Additional Notes: The author is partially supported by the NSF grants DMS 0753991 and DMS 0854949 and by the Clay Mathematics Institute as a Senior Scholar while preparing this work.
  • © Copyright 2012 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 25 (2012), 813-826
  • MSC (2010): Primary 14K02, 11G05, 11G10; Secondary 11F25, 11F33, 11F80
  • DOI:
  • MathSciNet review: 2904574