منابع مشابه
Split Reductions of Simple Abelian Varieties
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 Xp is absolutely simple for almost all primes p. Conversely, if the absolute endomorphism ring of X is noncommutative, then Xp is reducible for p in a set of positive density. An absolutely simple abelian variety ...
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Let X/K be an absolutely simple abelian variety over a number field; we study whether the reductions Xp tend to be simple, too. We show that if End(X) is a definite quaternion algebra, then the reduction Xp is geometrically isogenous to the self-product of an absolutely simple abelian variety for p in a set of positive density, while if X is of Mumford type, then Xp is simple for almost all p. ...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 2006
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.2508