Torsion order of smooth projective surfaces

Abstract

To a smooth projective variety $X$ whose Chow group of $0$-cycles is $\mathbf{Q}$-universally trivial one can associate its torsion index $\mathrm{Tor}(X)$, the smallest multiple of the diagonal appearing in a cycle-theoretic decomposition à la Bloch-Srinivas. We show that $\mathrm{Tor}(X)$ 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 $k$.

A few more minor changes in Colliot-Thélène's appendix

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