Perucca, Antonella2011-12-162011-12-162011-12-16201110.1093/imrn/rnq080https://infoscience.epfl.ch/handle/20.500.14299/74514WOS:000286472400003Let 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.Linear-DependenceOrderMapstext::journal::journal article::research article