The homotopy theory of cyclotomic spectra

@article{Blumberg2013TheHT,
  title={The homotopy theory of cyclotomic spectra},
  author={Andrew J. Blumberg and Michael A. Mandell},
  journal={arXiv: K-Theory and Homology},
  year={2013}
}
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). 
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