A finiteness theorem for zero-cycles over $p$-adic fields (with an appendix by Uwe Jannsen: Resolution of singularities for embedded curves)

Abstract

Let $R$ be a henselian discrete valuation ring. Let $X$ be a regular projective flat scheme over $\operatorname{Spec}(R)$ with generalized semistable reduction. We prove a bijectivity theorem for étale 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.