The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Commentarii Mathematici Helvetici


Full-Text PDF (285 KB) | Metadata | Table of Contents | CMH summary
Online access to the full text of Commentarii Mathematici Helvetici is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 92, Issue 4, 2017, pp. 839–857
DOI: 10.4171/CMH/426

Published online: 2017-10-24

Torsion order of smooth projective surfaces (with an appendix by J.-L. Colliot-Thélène)

Bruno Kahn[1]

(1) Université Pierre et Marie Curie, Paris, France

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 $k$.

Keywords: 0-cycles, birational invariants, birational motives

Kahn Bruno: Torsion order of smooth projective surfaces (with an appendix by J.-L. Colliot-Thélène). Comment. Math. Helv. 92 (2017), 839-857. doi: 10.4171/CMH/426