Zero-cycles on an arithmetic surface - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T05:46:50Z http://mathoverflow.net/feeds/question/61763 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/61763/zero-cycles-on-an-arithmetic-surface Zero-cycles on an arithmetic surface Andreas Holmstrom 2011-04-14T23:50:36Z 2011-04-15T01:47:56Z <p>Could anyone give a reference for the following statement, which I believe is true.</p> <p>"Let X be a regular scheme, flat over \$Spec( \mathbb{Z}) \$, with fiber dimension \$1\$. Then the Chow group \$CH^2(X)\$ is finite."</p> http://mathoverflow.net/questions/61763/zero-cycles-on-an-arithmetic-surface/61771#61771 Answer by SGP for Zero-cycles on an arithmetic surface SGP 2011-04-15T01:19:12Z 2011-04-15T01:47:56Z <p>The finiteness is known; see <a href="http://www.renyi.hu/~szamuely/bour09.pdf" rel="nofollow">Szamuely's Seminaire Bourbaki expose</a> and Remarque 3.4 (5) on page 11 is a precise reference. </p>