The multilinear support problem for products of abelian varieties and tori

2009/03/04 by Perucca, Antonella
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0903.0817

Abstract

Let G be the product of an abelian variety and a torus defined over a number field K. The aim of this paper is detecting the dependence among some given rational points of G by studying their reductions modulo all primes of K. We show that if some simple conditions on the order of the reductions of the points are satisfied then there must be a dependency relation over the ring of K-endomorphisms of G. We generalize Larsen's result on the support problem to several points on products of abelian varieties and tori.

Related

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• On the problem of detecting linear dependence for products of abelian varieties and tori
• A refined counter-example to the support conjecture for abelian\n varieties
• On the reduction of points on abelian varieties and tori
• The constant of the support problem for abelian varieties