The homotopy theory of cyclotomic spectra

Blumberg, Andrew J¹ ; Mandell, Michael A²

¹ Department of Mathematics, The University of Texas, Austin, TX 78712, USA
² Department of Mathematics, Indiana University, Rawles Hall, 831 E 3rd St, Bloomington, IN 47405, USA

Geometry & topology, Tome 19 (2015) no. 6, pp. 3105-3147.

Résumé

We describe spectral model category structures on the categories of cyclotomic spectra and $p$–cyclotomic spectra (in orthogonal spectra) with triangulated homotopy categories. We show that the functors $\mathit{TR}$ and $\mathit{TC}$ are corepresentable in these categories. Specifically, the derived mapping spectrum out of the sphere spectrum in the category of cyclotomic spectra corepresents the finite completion of $\mathit{TC}$ and the derived mapping spectrum out of the sphere spectrum in the category of $p$–cyclotomic spectra corepresents the $p$–completion of $\mathit{TC}\left(-;p\right)$.

Détail

DOI : 10.2140/gt.2015.19.3105

Classification : 19D55, 18G55, 55Q91
Keywords: topological cyclic homology, cyclotomic spectrum, model category, ABC category

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