Comptes Rendus
no. 11
Number theory/Algebraic geometry
The first cohomology of separably rationally connected varieties
[Le premier groupe de cohomologie des variétés séparablement, rationnellement connexes]

Présenté par : Claire Voisin

Frank Gounelas1
1 Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 871-873.

Nous présentons deux démonstrations de la nullité de H1(X,OX) 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.

We present two proofs that for a smooth projective separably rationally connected variety over an algebraically closed field H1(X,OX)=0. The second, cohomological proof generalises to varieties admitting a free curve of higher genus.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.09.013
Frank Gounelas 1

1 Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany 
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Frank Gounelas. The first cohomology of separably rationally connected varieties. Comptes Rendus. Mathématique, Volume 352 (2014) no. 11, pp. 871-873. doi : 10.1016/j.crma.2014.09.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.013/

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