21 citations · 35 across the 5 of their papers we have counts for
5 papers · 1 filter
On the reduction of points on 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 R_1,..., R_n be points in G(K). Let l be a rational prime and let a_1,..., a_n be non-nega…
A counterexample to the local-global principle of linear dependence for abelian varieties
Peter Jossen, Antonella Perucca
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 in 2002 asked whether it is true that the point P belongs…
On the problem of detecting linear dependence 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 R be a point in G(K) and let L be a finitely generated subgroup of G(K). Suppose that for…
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 th…
Prescribing valuations of the order of a point in the reductions 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 R be a K-rational point on G of infinite order. Call n_R the number of connected component…