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Title: Prescribing valuations of the order of a point in the reductions of abelian varieties and tori
Authors: Perucca, Antonella # ×
Issue Date: Feb-2009
Publisher: Academic Press
Series Title: Journal of Number Theory vol:129 issue:2 pages:469-476
Abstract: Let G be the product of an abelian variety and a torus defined over a number field K. Let R be a K-rational point on G of infinite order. Call n_R the number of connected components of the smallest algebraic K -subgroup of G to which R belongs. We prove that n_R is the greatest positive integer which divides the order of (R mod p) for all but finitely many primes p of K . Furthermore, let m > 0 be
a multiple of n R and let S be a finite set of rational primes. Then there exists a positive Dirichlet density of primes p of K such that for every ℓ in S the ℓ-adic valuation of the order of (R mod p) equals v_ℓ(m).
Description: http://arxiv.org/abs/0712.2812
ISSN: 0022-314X
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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