Geodesic
On the structure theory of the Iwasawa algebra of a p-adic Lie group
Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 271-311.

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This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa algebra, i.e. the completed group algebra, 6 of a p-adic analytic group G. For G without any p-torsion element we prove that 6 is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null 6-module. This is classical when G=Êkp for some integer kS1, but was previously unknown in the non-commutative case. Then the category of 6-modules up to pseudo-isomorphisms is studied and we obtain a weak structure theorem for the Êp-torsion part of a finitely generated 6-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
DOI : 10.1007/s100970100038
Classification : 16-XX, 00-XX
Keywords: 
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     title = {On the structure theory of the {Iwasawa} algebra of a p-adic {Lie} group},
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Otmar Venjakob. On the structure theory of the Iwasawa algebra of a p-adic Lie group. Journal of the European Mathematical Society, Tome 4 (2002) no. 3, pp. 271-311. doi : 10.1007/s100970100038. http://geodesic.mathdoc.fr/articles/10.1007/s100970100038/

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