Patchkoria, Irakli, Roitzheim, Constanze (2020) Rigidity and exotic models for v1-local G-equivariant stable homotopy theory. Mathematische Zeitschrift, 295 . pp. 839-875. ISSN 0025-5874. (doi:10.1007/s00209-019-02364-z) (KAR id:75354)
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Official URL: http://dx.doi.org/10.1007/s00209-019-02364-z |
Abstract
We prove that the v1-local G-equivariant stable homotopy category for G a finite group has a unique G-equivariant model at p=2. This means that at the prime 2 the homotopy theory of G-spectra up to fixed point equivalences on K-theory is uniquely determined by its triangulated homotopy category and basic Mackey structure. The result combines the rigidity result for K-local spectra of the second author with the equivariant rigidity result for G-spectra of the first author. Further, when the prime p is at least 5 and does not divide the order of G, we provide an algebraic exotic model as well as a G-equivariant exotic model for the v1-local G-equivariant stable homotopy category, showing that for primes p≥5 equivariant rigidity fails in general.
Item Type: | Article |
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DOI/Identification number: | 10.1007/s00209-019-02364-z |
Subjects: | Q Science > QA Mathematics (inc Computing science) |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Constanze Roitzheim |
Date Deposited: | 16 Jul 2019 08:27 UTC |
Last Modified: | 04 Jul 2023 12:55 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/75354 (The current URI for this page, for reference purposes) |
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