Split reductions of simple abelian varieties
Number Theory
2020-02-28 v2
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.
Cite
@article{arxiv.0806.4421,
title = {Split reductions of simple abelian varieties},
author = {Jeff Achter},
journal= {arXiv preprint arXiv:0806.4421},
year = {2020}
}
Comments
14 pages