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Comptes Rendus Mathématique
Volume 352, n° 11
pages 871-873 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.013
Received : 30 June 2014 ;  accepted : 18 September 2014
The first cohomology of separably rationally connected varieties
Le premier groupe de cohomologie des variétés séparablement, rationnellement connexes

Frank Gounelas
 Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany 


We present two proofs that for a smooth projective separably rationally connected variety over an algebraically closed field  . The second, cohomological proof generalises to varieties admitting a free curve of higher genus.

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Nous présentons deux démonstrations de la nullité de   pour les variétés projectives, lisses, séparablement rationnellement connexes, sur un corps algébriquement clos. La seconde, cohomologique, se généralise aux variétés ayant une courbe libre de genre supérieur.

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