Comptes Rendus
no. 1-2
Algebra/Homological Algebra
Homological properties of noncommutative Iwasawa algebras
[Propriétés homologiques des algèbres d'Iwasawa non commutatives]

Présenté par : Christophe Soulé

Feng Wei1
1 Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China
Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 15-20.

Pour tout groupe de Lie G p-adique compact, l'algèbre d'Iwasawa ΛG et son image épimorphique ΩG sont des algèbres d'Artin–Schelter Gorenstein. Nous montrons la formule d'Auslander–Buchsbaum, le théorème de Bass et le théorème des « non trous » pour des modules noethériens sur ΩG, ainsi que des versions duales pour leur modules artiniens. Il est montré que ΩG est auto-duale au sens de Morita par des complexes dualisants. Finalement, nous considérons les invariants homologiques « grade » des modules filtrés sur ΛG et ΩG, lorsque G est un groupe uniforme pro-p satisfaisant certaines propriétés.

For any compact p-adic Lie group G, the Iwasawa algebra ΩG is an Artin–Schelter Gorenstein algebra. We obtain the Auslander–Buchsbaum formula, the Bass's theorem and the No-holes theorem for noetherian modules over ΛG and ΩG, and the dual versions for their artinian modules. It is shown that ΩG is Morita self-dual via dualizing complexes. We finally consider the homological invariant “grade” of filtered modules over ΛG and ΩG, when G is a uniform pro-p group with certain properties.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.11.030
Feng Wei 1

1 Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China 
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Feng Wei. Homological properties of noncommutative Iwasawa algebras. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 15-20. doi : 10.1016/j.crma.2010.11.030. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.030/

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