Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Torsion order of smooth projective surfaces   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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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org