Purity of $ {G}_{2}$-torsors

Vladimir Chernousov; Ivan Panin

doi:10.1016/j.crma.2007.07.018

Group Theory/Algebraic Geometry

Purity of

G_{2}

-torsors

Presented by: Jean-Pierre Serre

Vladimir Chernousov ¹; Ivan Panin ^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

Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 307-312.

Abstract
Résumé

Let k be a field of characteristic zero, and let G be a split simple algebraic group of type $G_{2}$ over k. We prove that the functor $R \mapsto H_{\overset{´}{e} t}^{1} (R, G)$ of G-torsors satisfies purity for regular local rings containing k.

Soit k un corps de caractéristique 0, et soit G un k-groupe simple déployé de type $G_{2}$ . Nous montrons que le foncteur des G-torseurs satisfait au « théorème de pureté » pour la catégorie des anneaux locaux réguliers contenant k.

Received: 2007-06-18
Accepted: 2007-07-26
Published online: 2007-09-04

DOI: 10.1016/j.crma.2007.07.018

Author's affiliations:

Vladimir Chernousov ¹; Ivan Panin ^{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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     author = {Vladimir Chernousov and Ivan Panin},
     title = {Purity of $ {G}_{2}$-torsors},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {307--312},
     publisher = {Elsevier},
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     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.07.018},
     language = {en},
}

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Vladimir Chernousov; Ivan Panin. Purity of $ {G}_{2}$-torsors. Comptes Rendus. Mathématique, Volume 345 (2007) no. 6, pp. 307-312. doi : 10.1016/j.crma.2007.07.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.07.018/

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