A twisted Bass-Heller-Swan decomposition for localising invariants
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 an...
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Zusammenfassung: | 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. |
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DOI: | 10.48550/arxiv.2410.22877 |