The homotopy theory of cyclotomic spectra

By Andrew Justin Blumberg, Michael A. Mandell. 2013

47 citations recorded by the source corpus.

We describe spectral model* categories of cyclotomic spectra and p-cyclotomic spectra (in orthogonal spectra) with triangulated homotopy categories. In the homotopy category of cyclotomic spectra, the spectrum of maps from the sphere spectrum corepresents the finite completion of TC, and in the homotopy category of p-cyclotomic spectra, the spectrum of maps from the sphere spectrum corepresents the p-completion of TC(-;p).

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9896f22f064fca4dbad310ae90ba02d3503130e0

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

p-ADIC GEOMETRY (2017, background): “Theorem 8.4 ([NS17]). On respective subcategories of bounded below objects, the 1-category of cyclotomic spectra (in the sense of Hesselholt-Madsen, [HM97], and made more precise by Blumberg-Mandell, [BM15]) is equivalent to the 1-category of naively T-equivariant spectra Stogether with a T-equivari”
Uniqueness of the multiplicative cyclotomic trace (2011, background): “The unique homotopy class of maps of ∞ Fun(Cat ∞ , ∞ ) from K to TC that restrict to maps of E ∞ algebras K TC n”
K-theory and topological cyclic homology of henselian pairs (2018, result): “Introduced originally by Bökstedt– Hsiang–Madsen [13], nowadays there are several treatments of CycSp by various authors, including Blumberg–Mandell [12], Barwick–Glasman [6], Nikolaus–Scholze [60], and Ayala–Mazel-Gee– Rozenblyum [5].”