### Beilinson's Tate conjecture for K_2 and finiteness of torsion zero-cycles on elliptic surface, by Masanori Asakura and Kanetomo Sato

In this paper, we study an analogue of the Tate conjecture for K_2 of U the
complement of split multiplicative fibers in an elliptic surface. A main result
is to give an upper bound of the rank of the Galois fixed part of the etale
cohomology H^2(\bar{U},Q_p(2)). As an application, we give an elliptic K3
surface X over a p-adic field for which the torsion part of the Chow group
CH_0(X) of 0-cycles is finite. This would be the first example of a surface
X over a p-adic field whose geometric genus is non-zero and for which the
torsion part of CH_0(X) is finite.

Masanori Asakura <not-available>

Kanetomo Sato <kanetomo@math.nagoya-u.ac.jp>