Galois sections for abelian varieties over number fields

For an abelian variety A over a number field k, we discuss the space of sections of its fundamental group extension pi(1)(A/k). By analyzing the maximal divisible subgroup of H-1(k, A) we show that the space of sections of pi(1) (A/k) contains a copy of (Z) over cap ([k:Q].dim(A)) and is never in bijection with A(k). This is essentially a result about the structure of H-1(k, T-l (A)).