no. 6
Group Theory/Algebraic Geometry
Purity of G2-torsors
[Un théorème de pureté pour les G2-torseurs]

Présenté par : Jean-Pierre Serre

Chernousov, Vladimir1 ; Panin, Ivan2, 3
1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 SFB-701 at Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
3 Steklov Mathematical Institute at St. Petersburg, Fontanka 27, 191023 St. Petersburg, Russia
Comptes Rendus. Mathématique, Tome 345 (2007) no. 6, pp. 307-312.

Soit k un corps de caractéristique 0, et soit G un k-groupe simple déployé de type G2. Nous montrons que le foncteur des G-torseurs satisfait au « théorème de pureté » pour la catégorie des anneaux locaux réguliers contenant k.

Let k be a field of characteristic zero, and let G be a split simple algebraic group of type G2 over k. We prove that the functor R↦He´t1(R,G) of G-torsors satisfies purity for regular local rings containing k.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.07.018
Chernousov, Vladimir 1 ; Panin, Ivan 2, 3

1 Department of Mathematics, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
2 SFB-701 at Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
3 Steklov Mathematical Institute at St. Petersburg, Fontanka 27, 191023 St. Petersburg, Russia 
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Chernousov, Vladimir; Panin, Ivan. Purity of $ {G}_{2}$-torsors. Comptes Rendus. Mathématique, Tome 345 (2007) no. 6, pp. 307-312. doi : 10.1016/j.crma.2007.07.018. http://www.numdam.org/articles/10.1016/j.crma.2007.07.018/

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