Prime ideals in nilpotent Iwasawa algebras

Author: 

Ardakov, K

Publication Date: 

9 February 2012

Journal: 

Inventiones Mathematicae

Last Updated: 

2019-08-14T01:10:11.433+01:00

Issue: 

2

Volume: 

190

DOI: 

10.1007/s00222-012-0385-4

page: 

439-503

abstract: 

Let G be a nilpotent complete p-valued group of finite rank and let k be a
field of characteristic p. We prove that every faithful prime ideal of the
Iwasawa algebra kG is controlled by the centre of G, and use this to show that
the prime spectrum of kG is a disjoint union of commutative strata. We also
show that every prime ideal of kG is completely prime. The key ingredient in
the proof is the construction of a non-commutative valuation on certain
filtered simple Artinian rings.

Symplectic id: 

399409

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article