Summary: PRIME IDEALS IN NILPOTENT IWASAWA ALGEBRAS
Abstract. Let G be a nilpotent complete pvalued 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 noncommutative valuation on
certain filtered simple Artinian rings.
1. Introduction 1
2. Preliminaries 5
3. The construction of a noncommutative valuation 6
4. Automorphisms of pvalued groups 16
5. #primes and open subgroups 22
6. The Mahler expansion of an automorphism 26
7. Control theorem for faithful prime ideals 32
8. Applications 41