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• W1983127114 abstract "Consider a point of infinite order on an abelian variety over a number field. Then its reduction at any place v of good reduction is a torsion point. For most of this paper we fix a rational prime ℓ and study how the ℓ-part of this reduction varies with v. Under suitable conditions we prove various statements on this ℓ-part for all v in a set of positive Dirichlet density: for example that its order is a fixed power of ℓ, that its order is non-trivial for the reductions of finitely many points, or that its order is larger than a certain explicit value that varies with v. By similar methods we prove that for all v in a set of positive Dirichlet density the reduction of a given abelian variety possesses no non-trivial supersingular abelian subvariety." @default.
• W1983127114 created "2016-06-24" @default.
• W1983127114 creator A5086491060 @default.
• W1983127114 date "2004-06-23" @default.
• W1983127114 modified "2023-10-18" @default.
• W1983127114 title "On the order of the reduction of a point on an abelian variety" @default.
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• W1983127114 doi "https://doi.org/10.1007/s00208-004-0548-8" @default.
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