no. 9
Lie Algebras/Group Theory
Vanishing of H1 for Dedekind rings and applications to loop algebras
[Trivialité de H1 pour les anneaux de Dedekind, applications aux algèbres de lacets]

Présenté par : Jacques Tits

Pianzola, Arturo1
1 Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 633-638.

Nous établissons une version de la « Conjecture I » de Serre pour les anneaux de Dedekind. Ceci nous permet de décrire les algèbres de lacets tordues en termes de torseurs.

We establish a version of Serre's ‘Conjecture I’ for Dedekind domains. As an application, we give a parametrization of twisted loop algebras by means of torsors.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.03.022
Pianzola, Arturo 1

1 Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada 
@article{CRMATH_2005__340_9_633_0,
     author = {Pianzola, Arturo},
     title = {Vanishing of $ {H}^{1}$ for {Dedekind} rings and applications to loop algebras},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {633--638},
     publisher = {Elsevier},
     volume = {340},
     number = {9},
     year = {2005},
     doi = {10.1016/j.crma.2005.03.022},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.03.022/}
}
TY  - JOUR
AU  - Pianzola, Arturo
TI  - Vanishing of $ {H}^{1}$ for Dedekind rings and applications to loop algebras
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 633
EP  - 638
VL  - 340
IS  - 9
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.crma.2005.03.022/
DO  - 10.1016/j.crma.2005.03.022
LA  - en
ID  - CRMATH_2005__340_9_633_0
ER  - 
%0 Journal Article
%A Pianzola, Arturo
%T Vanishing of $ {H}^{1}$ for Dedekind rings and applications to loop algebras
%J Comptes Rendus. Mathématique
%D 2005
%P 633-638
%V 340
%N 9
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.crma.2005.03.022/
%R 10.1016/j.crma.2005.03.022
%G en
%F CRMATH_2005__340_9_633_0
Pianzola, Arturo. Vanishing of $ {H}^{1}$ for Dedekind rings and applications to loop algebras. Comptes Rendus. Mathématique, Tome 340 (2005) no. 9, pp. 633-638. doi : 10.1016/j.crma.2005.03.022. http://archive.numdam.org/articles/10.1016/j.crma.2005.03.022/

[1] Allison, B.; Berman, S.; Pianzola, A. Covering algebras II: Isomorphism of loop algebras, J. Reine Angew. Math., Volume 571 (2004), pp. 39-71

[2] Colliot-Thélène, J.-L.; Sansuc, J.-J. Principal homogeneous spaces under flasque tori: applications, J. Algebra, Volume 106 (1987), pp. 148-205

[3] Demazure, M.; Gabriel, P. Groupes Algébriques, North-Holland, 1970

[4] Demazure, M.; Grothendieck, A. Schémas en groupes (SGA3), Lecture Notes in Math., vol. 151–153, Springer-Verlag, Berlin, 1970

[5] Douai, J.-C. Espaces homogènes et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind, J. Théor. Nombres Bordeaux, Volume 7 (1995), pp. 21-26

[6] Giraud, J. Cohomologie non-Abélienne, Springer, 1971

[7] Grantcharov, D.; Pianzola, A. Automorphisms and loop algebras of finite-dimensional simple Lie superalgebras, Inter. Math. Res. Not., Volume 73 (2004), pp. 3937-3962

[8] Grothendieck, A. Revêtements étales et groupe fondamental (SGA1), Lecture Notes in Math., vol. 224, Springer-Verlag, Berlin, 1971

[9] Kac, V. Infinite-Dimensional Lie Algebras, Cambridge University Press, Cambridge, 1990

[10] Pianzola, A. Affine Kac–Moody Lie algebras as torsors over the punctured line, Indag. Math., Volume 13 (2002), pp. 249-257

[11] Serre, J.-P. Galois Cohomology, Springer, 1997

Cité par Sources :