(1) Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
Abstract:
Let C1,···,Cd be Mumford curves defined over a finite extension of and let X=C1×···×Cd. We shall show the following: (1) The cycle map CH0(X)/n → H2d(X, μn⊗d) is injective for any non-zero integer n. (2) The kernel of the canonical map CH0(X)→Hom(Br(X),) (defined by the Brauer-Manin pairing) coincides with the maximal divisible subgroup in CH0(X).