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 ...
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 ...
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 ...
