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

Abstract

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 $k$.