Selmer group associated to the Chow group of certain codimension two cycles

Let X be a surface with geometric genus and irregularity zero which is defined over a number field K. Let X denote a smooth spread of X over O K [1/f] for some element f ∈ O K and A 2 stands for the group of algebraically trivial cycles on schemes modulo rational equivalence. If j∗ : A 2 (X) → A 2 (X) be the flat pull-back corresponding to the embedding j : X ,→ X then we prove that im(j∗)(K)/A 2 (X)(K) is a torsion group. Here im(j∗)(K),A 2 (X)(K) stand for the cycles fixed under the action of the absolute Galois group.