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Rigidity and exotic models for v1-local G-equivariant stable homotopy theory

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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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
DOI/Identification number: 10.1007/s00209-019-02364-z
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Constanze Roitzheim
Date Deposited: 16 Jul 2019 08:27 UTC
Last Modified: 20 May 2020 11:21 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/75354 (The current URI for this page, for reference purposes)
Roitzheim, Constanze: https://orcid.org/0000-0003-3065-0672
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