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research article
On the Reduction of Points on Abelian Varieties and Tori
Perucca, Antonella
Let G be the product of an abelian variety and a torus defined over a number field K. Let R-1, ..., R-n be points in G(K). Let l be a rational prime, and let a(1), ..., a(n) be nonnegative integers. Consider the set of primes p of K satisfying the following condition: the l-adic valuation of the order of (R-i mod p) equals a(i) for every i = 1, ..., n. We show that this set is either finite or has a positive natural density. We characterize the n-tuples a(1), ..., a(n) for which the density is positive. More generally, we study the l-part of the reduction of the points.
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Type
research article
Web of Science ID
WOS:000286472400003
Authors
Perucca, Antonella
Publication date
2011
Published in
Start page
293
End page
308
Subjects
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 16, 2011