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arXiv · 1605.01762

Torsion order of smooth projective surfaces

Bruno Kahn·with an appendix by Jean-Louis Colliot-Thélène
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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 \`a la Bloch-Srinivas. We show that $\mathrm{Tor}(X)$ is the exponent of the torsion in the N\'eron-Severi-group of $X$ when $X$ is a surface over an algebraically closed field $k$, up to a power of the exponential characteristic of $k$.

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Bruno Kahn, with an appendix by Jean-Louis Colliot-Thélène. 2016-05-05. Torsion order of smooth projective surfaces. https://doi.org/10.4171/cmh/426

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