Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sur la conjecture de Tate enti\`ere pour le produit d'une courbe et
  d'une surface $CH_{0}$-triviale sur un corps fini   We investigate a strong version of the integral Tate conjecture for 1-cycles
on the product of a curve and a surface over a finite field, under the
assumption that the surface is geometrically $CH_0$-trivial. By this we mean
that over any algebraically closed field extension, the degree map on the
zero-dimensional Chow group of the surface is an isomorphism. This applies to
Enriques surfaces. When the N\'eron-Severi group has no torsion, we recover
earlier results of A. Pirutka. The results rely on a detailed study of the
third unramified cohomology group of specific products of varieties.

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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas