Cohomologie non ramifiée et conjecture de Hodge entière

  title={Cohomologie non ramifi{\'e}e et conjecture de Hodge enti{\`e}re},
  author={Jean-Louis Colliot-Th'elene and Claire Voisin},
  journal={Duke Mathematical Journal},
Building upon the Bloch–Kato conjecture in Milnor K-theory, we relate the third unramified cohomology group with Q/Z coefficients with a group which measures the failure of the integral Hodge conjecture in degree 4. As a first consequence, a geometric theorem of the second-named author implies that the third unramified cohomology group with Q/Z coefficients vanishes on all uniruled threefolds. As a second consequence, a 1989 example by Ojanguren and the first named author implies that the… 
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