Global algebraic K‐theory

We introduce a global equivariant refinement of algebraic K‐theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global Ω$\Omega$‐spectrum that keeps track of genuine G$G$‐equivar...

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Bibliographic Details
Published in:Journal of topology 2022-09, Vol.15 (3), p.1325-1454
Main Author: Schwede, Stefan
Format: Article
Language:English
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Summary:We introduce a global equivariant refinement of algebraic K‐theory; here ‘global equivariant’ refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global Ω$\Omega$‐spectrum that keeps track of genuine G$G$‐equivariant infinite loop spaces, for all finite groups G$G$. The resulting global algebraic K‐theory spectrum is a rigid way of packaging the representation K‐theory, or ‘Swan K‐theory’ into one highly structured object.
ISSN:1753-8416
1753-8424
DOI:10.1112/topo.12241