EUDML

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On the structure theory of the Iwasawa algebra of a p-adic Lie group

Otmar Venjakob — 2002

Journal of the European Mathematical Society

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, $Λ$ of a $p$ -adic analytic group $G$ . For $G$ without any $p$ -torsion element we prove that $Λ$ is an Auslander regular ring. This result enables us to give a good definition of the notion of a pseudo-null $Λ$ -module. This is classical when $G = ℤ_{p}^{k}$ for some integer $k \geq 1$ , but was previously unknown in the non-commutative case. Then the category of $Λ$ -modules...

The GL2 main conjecture for elliptic curves without complex multiplication

John Coates; Takako Fukaya; Kazuya Kato; Ramdorai Sujatha; Otmar Venjakob — 2005

Publications Mathématiques de l'IHÉS

Let G be a compact -adic Lie group, with no element of order , and having a closed normal subgroup H such that G/H is isomorphic to . We prove the existence of a canonical Ore set S of non-zero divisors in the Iwasawa algebra Λ(G) of G, which seems to be particularly relevant for arithmetic applications. Using localization with respect to S, we are able to define a characteristic element for every finitely generated Λ(G)-module M which has the property that the quotient of M by its...