Contents Online
Mathematical Research Letters
Volume 16 (2009)
Number 2
Split reductions of simple abelian varieties
Pages: 199 – 213
DOI: https://dx.doi.org/10.4310/MRL.2009.v16.n2.a1
Author
Abstract
Consider an absolutely simple abelian variety $X$ over a number field $K$. We show that if the absolute endomorphism ring of $X$ is commutative and satisfies certain parity conditions, then $X_\idp$ is absolutely simple for almost all primes $\idp$. Conversely, if the absolute endomorphism ring of $X$ is noncommutative, then $X_\idp$ is reducible for $\idp$ in a set of positive density.
Published 1 January 2009