A finiteness property of abelian varieties with potentially ordinary good reduction

Hida, Haruzo

doi:10.1090/S0894-0347-2012-00730-9

A finiteness property of abelian varieties with potentially ordinary good reduction
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by Haruzo Hida

J. Amer. Math. Soc. 25 (2012), 813-826

DOI: https://doi.org/10.1090/S0894-0347-2012-00730-9

Published electronically: January 25, 2012

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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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