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A finiteness property of abelian varieties with potentially ordinary good reduction


Author: Haruzo Hida
Journal: J. Amer. Math. Soc. 25 (2012), 813-826
MSC (2010): Primary 14K02, 11G05, 11G10; Secondary 11F25, 11F33, 11F80
DOI: https://doi.org/10.1090/S0894-0347-2012-00730-9
Published electronically: January 25, 2012
MathSciNet review: 2904574
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Abstract: 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
Email: hida@math.ucla.edu

DOI: https://doi.org/10.1090/S0894-0347-2012-00730-9
Keywords: Abelian variety, twist equivalence, Hecke algebra, Galois representation
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.
Article copyright: © Copyright 2012 American Mathematical Society

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