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On a Localisation Sequence for the K-Theory of Skew Power Series Rings

Published online by Cambridge University Press:  21 February 2013

Malte Witte
Malte Witte*
Affiliation:
Ruprecht-Karls-Universität Heidelberg, Mathematisches Institut, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germanywitte@mathi.uni-heidelberg.de
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Abstract

Let B = A[[t;σ,δ]] be a skew power series ring such that σ is given by an inner automorphism of B. We show that a certain Waldhausen localisation sequence involving the K-theory of B splits into short split exact sequences. In the case that A is noetherian we show that this sequence is given by the localisation sequence for a left denominator set S in B. If B = ℤp[[G]] happens to be the Iwasawa algebra of a p-adic Lie group G ≅ H ⋊ ℤp, this set S is Venjakob's canonical Ore set. In particular, our result implies that

is split exact for each n ≥ 0. We also prove the corresponding result for the localisation of ℤp[[G]][] with respect to the Ore set S*. Both sequences play a major role in non-commutative Iwasawa theory.

Keywords

Skew power series ringshigher K-theoryIwasawa algebras16W6016E2011R23

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Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 1 , February 2013 , pp. 125 - 154
Copyright
Copyright © ISOPP 2013

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