 
Summary: LOCALISATION AT AUGMENTATION IDEALS IN IWASAWA
ALGEBRAS
KONSTANTIN ARDAKOV
Abstract. Let G be a compact padic analytic group and let G be its
completed group algebra with coefficient ring the padic integers Zp. We
show that the augmentation ideal in G of a closed normal subgroup H of
G is localisable if and only if H is finitebynilpotent, answering a question
of Sujatha. The localisations are shown to be Auslanderregular 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 Fpversion G of G are controlled
by + , where + is the largest finite 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 padic analytic group and let G
and G denote the completed group algebras of G with coefficients in Zp and Fp,
respectively. Otherwise known as Iwasawa algebras, these rings were first defined
by Lazard [16] and have been the focus of increasing attention in recent years,
primarily because of their connections to number theory and arithmetic geometry.
We refer the reader to [11] and [12] for more information about these connections.
1.2. Iwasawa algebras also form a natural class of Noetherian algebras, analogous
