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Commentarii Mathematici Helvetici

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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