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

Irakli Patchkoria, Constanze Roitzheim* (Corresponding Author)

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)839-875
Number of pages37
JournalMathematische Zeitschrift
Volume295
Early online date12 Aug 2019
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • ALGEBRAIC MODEL
  • K-THEORY
  • CATEGORIES
  • SPECTRA
  • EQUIVALENCES
  • LOCALIZATION
  • FUNCTORS
  • RESPECT

ASJC Scopus subject areas

  • Mathematics(all)

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