Split reductions of simple abelian varieties

Details Split reductions of simple abelian varieties Split reductions of simple abelian varieties

2008-06-27

arxiv.org/abs/0806.4421v2

Mathematics

Number Theory

14 pages

Scientific paper

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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