The Adams isomorphism revisited

Bastiaan Cnossen; Tobias Lenz; Sil Linskens

doi:10.1007/s00209-024-03582-w

The Adams isomorphism revisited

Bastiaan Cnossen
, Tobias Lenz
, Sil Linskens^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable equivariantly semiadditive global category. This encompasses the well-known Adams isomorphism in equivariant stable homotopy theory, and applies more generally in the settings of G-Mackey functors, G-global homotopy theory, and equivariant Kasparov categories.

Original language	English
Article number	33
Journal	Mathematische Zeitschrift
Volume	308
Issue number	2
DOIs	https://doi.org/10.1007/s00209-024-03582-w
Publication status	Published - Oct 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Funding

B.C. thanks Ulrich Bunke and Benjamin Duenzinger for discussions on equivariant Kasparov categories. The authors would like to thank the referee for helpful comments, which led to the inclusion of Appendix C. During the preparation of this article, B.C. was supported by the Max Planck Institute for Mathematics in Bonn and the SFB 1085 'Higher Invariants' in Regensburg, funded by the DFG. S.L. is an associate member of the Hausdorff Center for Mathematics at the University of Bonn, and is supported by the DFG Schwerpunktprogramm 1786 'Homotopy Theory and Algebraic Geometry' (project ID SCHW 860/1-1).

Funders	Funder number
Max Planck Institute for Mathematics in Bonn
DFG	SFB 1085, SCHW 860/1-1, 1786

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AB - We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable equivariantly semiadditive global category. This encompasses the well-known Adams isomorphism in equivariant stable homotopy theory, and applies more generally in the settings of G-Mackey functors, G-global homotopy theory, and equivariant Kasparov categories.

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The Adams isomorphism revisited

Abstract

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