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.

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Authors

Shuji Saito

Department of Mathematical Sciences
University of Tokyo
8-1 Komaba 3-chome, Meguro-ku
Tokyo 153-8914
Japan

Kanetomo Sato

Graduate School of Mathematics
Nagoya University
Furocho, Chikusa-ku
Nagoya 464-8602
Japan

Uwe Jannsen

Fakultät für Mathematik
Universität Regensburg
Universitätsstr. 31
93040 Regensburg
Germany