Extensions of almost faithful prime ideals in virtually nilpotent mod-$p$ Iwasawa algebras

William Woods

Vol. 297 (2018), No. 2, 477–509

DOI: 10.2140/pjm.2018.297.477

Abstract

Let $G$ be a nilpotent-by-finite compact $p$-adic analytic group for some $p>2$, and $H={FN}_p\left(G\right)$ be its finite-by-(nilpotent $p$-valuable) radical. Fix a finite field $k$ of characteristic $p$, and write $kG$ for the completed group ring of $G$ over $k$. We show that almost faithful $G$-stable prime ideals $P$ of $kH$ extend to prime ideals $PkG$ of $kG$. This is a crucial building block in understanding the prime spectrum of $kG$.

Keywords

faithful prime ideals, nilpotent Iwasawa algebras

Mathematical Subject Classification 2010

Primary: 16D25, 16S34, 16S35, 16W60

Milestones

Received: 12 August 2017

Revised: 26 March 2018

Accepted: 28 April 2018

Published: 20 December 2018