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A twisted Bass-Heller-Swan decomposition for localising invariants

MPS-Authors
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Kirstein,  Dominik
Max Planck Institute for Mathematics, Max Planck Society;

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Kremer,  Christian
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.48550/arXiv.2410.22877
(Preprint)

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2410.22877.pdf
(Preprint), 329KB

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Citation

Kirstein, D., & Kremer, C. (submitted). A twisted Bass-Heller-Swan decomposition for localising invariants.


Cite as: https://hdl.handle.net/21.11116/0000-0010-02DC-4
Abstract
We generalise the classical Bass-Heller-Swan decomposition for the K-theory of (twisted) Laurent algebras to a splitting for general localising invariants of certain categories of twisted automorphisms. As an application, we obtain splitting formulas for Waldhausen's A-theory of mapping tori and for the K-theory of certain tensor algebras. We identify the Nil-terms appearing in this splitting in two ways. Firstly, as the reduced K-theory of twisted endomorphisms. Secondly, as the reduced K-theory of twisted nilpotent endomorphisms. Finally, we generalise classical vanishing results for Nil-terms of regular rings to our setting.