Propriétés homologiques des algèbres d'Iwasawa non commutatives

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 ΩG 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 ΩG and ΩG, when G is a uniform pro-p group with certain properties.