Publications by Antonella Perucca

On the Reduction of Points on Abelian Varieties and Tori

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 followin ...

2011

A counterexample to the local-global principle of linear dependence for Abelian varieties

Antonella Perucca, Peter Simon Jossen

Let A be an Abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) f ...

2010

On the problem of detecting linear dependence for products of abelian varieties and tori

Antonella Perucca

2010

Two variants of the support problem for products of abelian varieties and tori

Antonella Perucca

Let G be the product of an abelian variety and a torus defined over a number field K. Let P and Q be K-rational points on G. Suppose that for all but finitely many primes p of K the order of (Q mod p) divides the order of (P mod p). Then there exist a K-en ...

2009