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Summary: PRIME IDEALS IN NILPOTENT IWASAWA ALGEBRAS
KONSTANTIN ARDAKOV
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.
Contents
1. Introduction 1
2. Preliminaries 5
3. The construction of a non-commutative valuation 6
4. Automorphisms of p-valued 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
References 46
1. Introduction
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