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arXiv · 1912.08872

Global algebraic K-theory

Stefan Schwede
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Abstract

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 $Ω$-spectrum that keeps track of genuine $G$-equivariant infinite loop spaces, for all finite groups $G$. 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.

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Stefan Schwede. 2022-03-18. Global algebraic K-theory. https://doi.org/10.1112/topo.12241

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