 
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 nitebynilpotent, answering a question
of Sujatha. The localisations are shown to be Auslanderregular 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 dened
