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arXiv · 1701.04261

Troisi\`eme groupe de cohomologie non ramifi\'ee des hypersurfaces de Fano

Jean-Louis Colliot-Thélène
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Abstract

We establish the vanishing of the third unramified cohomology group for many types of Fano hypersurfaces in projective space over an algebraically closed field of arbitrary characteristic, and over a finite field. For cubic hypersurfaces over a finite field, the case of fourfolds remains open. --- Sur un corps alg\'ebriquement clos et sur un corps fini, on \'etablit de nouveaux r\'esultats d'annulation pour la cohomologie non ramifi\'ee de degr\'e 3 pour de nombreux types d'hypersurfaces de Fano. Le cas des hypersurfaces cubiques de dimension 4 sur un corps fini reste ouvert.

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Jean-Louis Colliot-Thélène. 2017-01-16. Troisi\`eme groupe de cohomologie non ramifi\'ee des hypersurfaces de Fano. https://arxiv.org/abs/1701.04261

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