Hostname: page-component-6b989bf9dc-vmcqm Total loading time: 0 Render date: 2024-04-14T16:37:24.056Z Has data issue: false hasContentIssue false

LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA ALGEBRAS

Published online by Cambridge University Press:  23 August 2006

KONSTANTIN ARDAKOV
Affiliation:
Christ's College, Cambridge e-mail: K.Ardakov@dpmms.cam.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let $G$ be a compact $p$-adic analytic group and let $\Lambda_G$ be its completed group algebra with coefficient ring the $p$-adic integers $\mathbb{Z}_p$. We show that the augmentation ideal in $\Lambda_G$ of a closed normal subgroup $H$ of $G$ is localisable if and only if $H$ is finite-by-nilpotent, answering a question of Sujatha. The localisations are shown to be Auslander-regular rings with Krull and global dimensions equal to dim $H$. It is also shown that the minimal prime ideals and the prime radical of the $\mathbb{F}_p$-version $\Omega_G$ of $\Lambda_G$ are controlled by $\Omega_{\Delta^+}$, where $\Delta^+$ is the largest finite normal subgroup of $G$. Finally, we prove a conjecture of Ardakov and Brown [1].

Type
Research Article
Copyright
2006 Glasgow Mathematical Journal Trust