[Le premier groupe de cohomologie des variétés séparablement, rationnellement connexes]
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.
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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@article{CRMATH_2014__352_11_871_0,
author = {Gounelas, Frank},
title = {The first cohomology of separably rationally connected varieties},
journal = {Comptes Rendus. Math\'ematique},
pages = {871--873},
publisher = {Elsevier},
volume = {352},
number = {11},
year = {2014},
doi = {10.1016/j.crma.2014.09.013},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.013/}
}
TY - JOUR AU - Gounelas, Frank TI - The first cohomology of separably rationally connected varieties JO - Comptes Rendus. Mathématique PY - 2014 SP - 871 EP - 873 VL - 352 IS - 11 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.09.013/ DO - 10.1016/j.crma.2014.09.013 LA - en ID - CRMATH_2014__352_11_871_0 ER -
%0 Journal Article %A Gounelas, Frank %T The first cohomology of separably rationally connected varieties %J Comptes Rendus. Mathématique %D 2014 %P 871-873 %V 352 %N 11 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.09.013/ %R 10.1016/j.crma.2014.09.013 %G en %F CRMATH_2014__352_11_871_0
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. http://www.numdam.org/articles/10.1016/j.crma.2014.09.013/
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