Geodesic
A finiteness theorem for zero-cycles over $p$-adic fields (with an appendix by Uwe Jannsen: Resolution of singularities for embedded curves)
Shuji Saito1 ; Kanetomo Sato2 ; Uwe Jannsen3
1 Department of Mathematical Sciences<br/>University of Tokyo<br/>8-1 Komaba 3-chome, Meguro-ku<br/>Tokyo 153-8914<br/>Japan
2 Graduate School of Mathematics<br/>Nagoya University<br/>Furocho, Chikusa-ku<br/>Nagoya 464-8602<br/>Japan
3 Fakultät für Mathematik<br/>Universität Regensburg<br/>Universitätsstr. 31<br/>93040 Regensburg<br/>Germany
Annals of mathematics, Tome 172 (2010) no. 3, pp. 1593-1639.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2010.172.1593

Shuji Saito 1 ; Kanetomo Sato 2 ; Uwe Jannsen 3

1 Department of Mathematical Sciences<br/>University of Tokyo<br/>8-1 Komaba 3-chome, Meguro-ku<br/>Tokyo 153-8914<br/>Japan
2 Graduate School of Mathematics<br/>Nagoya University<br/>Furocho, Chikusa-ku<br/>Nagoya 464-8602<br/>Japan
3 Fakultät für Mathematik<br/>Universität Regensburg<br/>Universitätsstr. 31<br/>93040 Regensburg<br/>Germany 
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     title = {A finiteness theorem for zero-cycles  over $p$-adic fields (with an appendix by {Uwe} {Jannsen:} {Resolution} of singularities for embedded curves)},
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Shuji Saito; Kanetomo Sato; Uwe Jannsen. A finiteness theorem for zero-cycles  over $p$-adic fields (with an appendix by Uwe Jannsen: Resolution of singularities for embedded curves). Annals of mathematics, Tome 172 (2010) no. 3, pp. 1593-1639. doi : 10.4007/annals.2010.172.1593. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1593/

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