- journal article metadata
European Mathematical Society Publishing House
2017-10-27 23:40:00
Commentarii Mathematici Helvetici
Comment. Math. Helv.
CMH
0010-2571
1420-8946
General
10.4171/CMH
http://www.ems-ph.org/doi/10.4171/CMH
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Swiss Mathematical Society
92
2017
4
Torsion order of smooth projective surfaces (with an appendix by J.-L. Colliot-Thélène)
Bruno
Kahn
Université Pierre et Marie Curie, Paris, France
0-cycles, birational invariants, birational motives
To a smooth projective variety $X$ whose Chow group of 0-cycles is $\mathbf Q$-universally trivial one can associate its torsion order Tor$(X)$, the smallest multiple of the diagonal appearing in a cycle-theoretic decomposition à la Bloch–Srinivas. We show that Tor$(X)$ is the exponent of the torsion in the Néron–Severi group of $X$ when $X$ is a surface over an algebraically closed field $k$, up to a power of the exponential characteristic of $k$.
Algebraic geometry
$K$-theory
839
857
10.4171/CMH/426
http://www.ems-ph.org/doi/10.4171/CMH/426