Cyclonic spectra, cyclotomic spectra, and a conjecture of Kaledin

Clark Barwick, Saul Glasman

Research output: Working paper


With an explicit, algebraic indexing (2, 1)-category, we develop an efficient homotopy theory of cyclonic objects: circle-equivariant objects relative to the family of finite subgroups. We construct an ∞-category of cyclotomic spectra as the homotopy fixed points of an action of the multiplicative monoid of the natural numbers on the category of cyclonic spectra. Finally, we elucidate and prove a conjecture of Kaledin on cyclotomic complexes.
Original languageEnglish
Number of pages28
Publication statusSubmitted - 5 Feb 2016


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