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

Gounelas, Frank1
1 Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
Comptes Rendus. Mathématique, Tome 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
Gounelas, Frank 1

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

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