Hoyois, Marc

Cdh Descent in Equivariant Homotopy \(K\)-Theory

Doc. Math. 25, 457-482 (2020)
DOI: 10.25537/dm.2020v25.457-482
Communicated by Mike Hill

Summary

We construct geometric models for classifying spaces of linear algebraic groups in \(G\)-equivariant motivic homotopy theory, where \(G\) is a tame group scheme. As a consequence, we show that the equivariant motivic spectrum representing the homotopy \(K\)-theory of \(G\)-schemes (which we construct as an \(E_\infty \)-ring) is stable under arbitrary base change, and we deduce that the homotopy \(K\)-theory of \(G\)-schemes satisfies cdh descent.

Mathematics Subject Classification

14F42, 14D23, 19D25, 14A20

Keywords/Phrases

algebraic \(K\)-theory, algebraic stacks

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Affiliation

Hoyois, Marc
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany

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