A naive approach to genuine $G$-spectra and cyclotomic spectra

Abstract

For any compact Lie group $G$, we give a description of genuine $G$-spectra in terms of the naive equivariant spectra underlying their geometric fixedpoints. We use this to give an analogous description of cyclotomic spectra in terms of naive $T$-spectra (where $T$ denotes the circle group), generalizing Nikolaus--Scholze's recent work in the eventually-connective case. We also give an explicit formula for the homotopy invariants of the cyclotomic structure on a cyclotomic spectrum in these terms.

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• The smooth Whitehead spectrum of a point at odd regular primes
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Cited by in corpus (7)

• On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra
• Integral Models for Spaces via the Higher Frobenius
• On the parametrized Tate construction
• A slice refinement of Bökstedt periodicity
• On the Dundas-Goodwillie-McCarthy theorem
• Recollements and stratification
• Natural symmetries of secondary Hochschild homology