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Summary: LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA
ALGEBRAS
KONSTANTIN ARDAKOV
Abstract. Let G be a compact p adic analytic group and let G be its
completed group algebra with coeÆcient ring the p adic integers Z p . We
show that the augmentation ideal in G of a closed normal subgroup H of
G is localisable if and only if H is nite-by-nilpotent, answering a question
of Sujatha. The localisations are shown to be Auslander-regular rings with
Krull and global dimensions equal to dimH. It is also shown that the minimal
prime ideals and the prime radical of the Fp
version
G of G are controlled
by
+ , where + is the largest nite normal subgroup of G. Finally, we
prove a conjecture of Ardakov and Brown[1].
1. Introduction
1.1. Iwasawa algebras. Let G be a compact p adic analytic group and let G
and
G denote the completed group algebras of G with coeÆcients in Z p and F p ,
respectively. Otherwise known as Iwasawa algebras, these rings were rst de ned
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