A finiteness theorem for zero-cycles overp-adic fields

Abstract

Let R be a henselian discrete valuation ring. Let X be a regular projective flat scheme over Spec (R) with generalized semistable reduction. We prove a bijectivity theorem for etale cycle class maps of the Chow group of 1-cycles on X. As an application, we prove a finiteness theorem for the Chow group of 0-cycles on a projective smooth variety over a p-adic field.