The homotopy theory of cyclotomic spectra

Abstract

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 $TR$ and $TC$ 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 $TC$ and the derived mapping spectrum out of the sphere spectrum in the category of $p$-cyclotomic spectra corepresents the $p$-completion of $TC(-;p)$.

This is a last draft version (May 5, 2015) of an article whose final version was first published in Geometry & Topology in 2015, published by Mathematical Sciences Publishers

References in corpus (1)

• Localization theorems in topological Hochschild homology and topological cyclic homology

Cited by in corpus (5)

• Kaledin's degeneration theorem and topological Hochschild homology
• Some recent advances in topological Hochschild homology
• Cyclification of Orbifolds
• Comparing cyclotomic structures on different models for topological Hochschild homology
• Assembly maps for topological cyclic homology of group algebras