Beilinson´s Tate conjecture for $K_2$ and finiteness of torsion zero-cycles on elliptic surfa

In this paper, we study an analogue of the Tate conjecture for K_2 of U, nthe complement of split multiplicative fibers in an elliptic surface. A main nresult is to give an upper bound of the rank of the Galois fixed part of the netale cohomology H^2( bar{U},Q_p(2)) . As an application, we give an elliptic nK3 surface X over a p-adic field for ..