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

David Ayala; Aaron Mazel-Gee; Nick Rozenblyum

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arXiv · 1710.06416

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

David Ayala·Aaron Mazel-Gee·Nick Rozenblyum

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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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David Ayala, Aaron Mazel-Gee, Nick Rozenblyum. 2017-10-17. A naive approach to genuine $G$-spectra and cyclotomic spectra. https://arxiv.org/abs/1710.06416

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