Split reductions of simple abelian varieties
نویسندگان
چکیده
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 ...
متن کاملExplicit bounds for split reductions of simple abelian varieties
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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This the original TEX file for my article Abelian Varieties, published as Chapter V of Arithmetic geometry (Storrs, Conn., 1984), 103–150, Springer, New York, 1986. The table of contents has been restored, some corrections have been made,1 there are minor improvements to the exposition, and an index has been added. The numbering is unchanged.
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2009
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2009.v16.n2.a1