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Title: On the reduction of points on abelian varieties and tori
Authors: Perucca, Antonella # ×
Issue Date: 2011
Publisher: Duke University Press
Series Title: International Mathematics Research Notices vol:2011 issue:7 pages:293-308
Abstract: Let G be the product of an abelian variety and a torus defined over a number field K . Let R1,...,Rn be points in G(K). Let ℓ be a rational prime, and let a1,...,an be nonnegative integers. Consider the set of primes p of K satisfying the following condition: the ℓ-adic valuation of the order of (Ri mod p) equals ai for every i=1,...,n. We show that this set is either finite or has a positive natural density. We characterize the n-tuples a1,...,an for which the density is positive. More generally, we study the ℓ-part of the reduction of the points.
Description: http://arxiv.org/abs/0909.4806
ISSN: 1073-7928
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Non-KU Leuven Association publications
× corresponding author
# (joint) last author

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