  Let A be an abelian variety over a number field F with End(A/F) commutative.
Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for
almost all places v of F the reduction of x modulo v lies in the reduction of S
modulo v. In this paper we prove that x must then lie in S + A(F)_tors. This
provides a partial answer to a generalization (due to W. Gajda) of the support
problem of Erdos.
