Abstract
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.
| Original language | English |
|---|---|
| Journal | Mathematische Zeitschrift |
| Early online date | 12 Aug 2019 |
| DOIs | |
| Publication status | E-pub ahead of print - 12 Aug 2019 |
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ASJC Scopus subject areas
- Mathematics(all)
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Rigidity and exotic models for v1-local G-equivariant stable homotopy. / Patchkoria, Irakli; Roitzheim, Constanze (Corresponding Author).
In: Mathematische Zeitschrift, 12.08.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Rigidity and exotic models for v1-local G-equivariant stable homotopy
AU - Patchkoria, Irakli
AU - Roitzheim, Constanze
N1 - The first author acknowledges the support of the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92), the German Research Foundation Schwerpunktprogramm 1786 and the Shota Rustaveli National Science Foundation Grant 217–614. He also thanks the Hausdorff Research Institute for Mathematics in Bonn for their hospitality. Finally the first author would like to thank Gijs Heuts, Akhil Mathew, Stefan Schwede and Christian Wimmer for helpful conversations. The second author thanks the Department of Mathematical Sciences in Copenhagen and the Hausdorff Research Institute for Mathematics in Bonn for their hospitality. Furthermore, the second author would like to thank David Barnes, Anna Marie Bohmann, John Greenlees and Mike Hill for useful discussions. We thank the referee for useful comments.
PY - 2019/8/12
Y1 - 2019/8/12
N2 - We prove that the v1-local G-equivariant stable homotopy category for Ga finite group has a unique G-equivariant model at p = 2. This means that at theprime 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.
AB - We prove that the v1-local G-equivariant stable homotopy category for Ga finite group has a unique G-equivariant model at p = 2. This means that at theprime 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.
UR - http://www.scopus.com/inward/record.url?scp=85070754970&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/rigidity-exotic-models-v1-v-1-local-gequivariant-stable-homotopy-theory
U2 - 10.1007/s00209-019-02364-z
DO - 10.1007/s00209-019-02364-z
M3 - Article
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
ER -