Localisation at augmentation ideals in Iwasawa algebras

Let G be a compact p-adic analytic group and let AG be its completed group algebra with coefficient ring the p-adic integers ℤ <inf>p</inf>. We show that the augmentation ideal in Λ <inf>G</inf> 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 double-struck F sign <inf>p</inf>-version Ω <inf>G</inf> of Λ <inf>G</inf> are controlled by Ω <inf>Δ</inf>+, where Δ ⁺ is the largest finite normal subgroup of G. Finally, we prove a conjecture of Ardakov and Brown [1]. © 2006 Glasgow Mathematical Journal Trust.