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 OK [1/f ] for some element f ∈ OK and A 2 stands for the group of algebraically trivial cycles on schemes modulo rational equivalence. If j∗ : A(X) → A(X) be the flat pull-back corresponding to the embedding j : X →֒ X then we prove that im(j)(K)/A(X)(K) is a torsion group. Here im(j∗)(K), A(X)(K) stand for the cycles fixed under the action of the absolute Galois group.