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Connections between the second Chow group of a smooth projective variety andits third unramified cohomology group, with coefficients the roots of unitytwisted twice, feature in several recent works. In this note we revisit a 1996paper by B. Kahn and specialize it to various types of rationally connectedvarieties.

Descente galoisienne sur le second groupe de Chow : mise au point et applications