Mackey functors and classical equivariant $K$-theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915447661658112 |
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| author | Lenz, Tobias |
| author_facet | Lenz, Tobias |
| contents | We show that the spectral Mackey functors associated to the equivariant algebraic $K$-theory spectra of Guillou-May and Merling (originally constructed using pointset models) can be described purely $\infty$-categorically in terms of the monoidal Borel construction of Barwick-Glasman-Shah and Hilman. We moreover show how Pützstück's global version of the Borel construction provides an analogous description of the global spectral Mackey functors arising from Schwede's global algebraic $K$-theory spectra.
Our arguments crucially rely on techniques from parametrized higher category theory as well as on structural results on global and equivariant $K$-theory to avoid any explicit computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mackey functors and classical equivariant $K$-theory Lenz, Tobias Algebraic Topology K-Theory and Homology 19D23, 55P91 (Primary), 18B10 (Secondary) We show that the spectral Mackey functors associated to the equivariant algebraic $K$-theory spectra of Guillou-May and Merling (originally constructed using pointset models) can be described purely $\infty$-categorically in terms of the monoidal Borel construction of Barwick-Glasman-Shah and Hilman. We moreover show how Pützstück's global version of the Borel construction provides an analogous description of the global spectral Mackey functors arising from Schwede's global algebraic $K$-theory spectra. Our arguments crucially rely on techniques from parametrized higher category theory as well as on structural results on global and equivariant $K$-theory to avoid any explicit computations. |
| title | Mackey functors and classical equivariant $K$-theory |
| topic | Algebraic Topology K-Theory and Homology 19D23, 55P91 (Primary), 18B10 (Secondary) |
| url | https://arxiv.org/abs/2508.11525 |