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Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: Un théorème de finitude pour la torsion. (The codimension two Chow group of varieties defined over a number field: A finiteness theorem for the torsion). (French) Zbl 0752.14004
Let \(X\) be a smooth projective variety defined over a number field and let \(CH^ 2(X)\) be the Chow group of codimension two cycles modulo rational equivalence. In this work, the authors show that if the cohomology group \(H^ 2(X,{\mathcal O}_ X)\) vanishes then the torsion group of \(CH^ 2(X)\) is a finite group.

14C05 Parametrization (Chow and Hilbert schemes)
14G25 Global ground fields in algebraic geometry
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