For any compact p-adic Lie group G, the Iwasawa algebra 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 and , and the dual versions for their artinian modules. It is shown that is Morita self-dual via dualizing complexes. We finally consider the homological invariant “grade” of filtered modules over and , when G is a uniform pro-p group with certain properties.
Pour tout groupe de Lie G p-adique compact, l'algèbre d'Iwasawa et son image épimorphique 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 , ainsi que des versions duales pour leur modules artiniens. Il est montré que est auto-duale au sens de Morita par des complexes dualisants. Finalement, nous considérons les invariants homologiques « grade » des modules filtrés sur et , lorsque G est un groupe uniforme pro-p satisfaisant certaines propriétés.
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Feng Wei 1
@article{CRMATH_2011__349_1-2_15_0, author = {Feng Wei}, title = {Homological properties of noncommutative {Iwasawa} algebras}, journal = {Comptes Rendus. Math\'ematique}, pages = {15--20}, publisher = {Elsevier}, volume = {349}, number = {1-2}, year = {2011}, doi = {10.1016/j.crma.2010.11.030}, language = {en}, }
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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