Split reductions of simple abelian varieties

Jeff Achter

doi:10.4310/mrl.2009.v16.n2.a1

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arXiv · 0806.4421

Split reductions of simple abelian varieties

Jeff Achter

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Abstract

Consider an absolutely simple abelian variety X over a number field K. If the absolute endomorphism ring of X is commutative and satisfies certain parity conditions, then the reduction X_p is absolutely simple for almost all p. Conversely, if the absolute endomorphism ring of X is noncommutative, then X_p is reducible for p in a set of positive density.

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Jeff Achter. 2009-02-26. Split reductions of simple abelian varieties. https://doi.org/10.4310/mrl.2009.v16.n2.a1

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