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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The homotopy theory of cyclotomic spectra

Andrew J Blumberg and Michael A Mandell

Geometry & Topology 19 (2015) 3105–3147
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).

Keywords
topological cyclic homology, cyclotomic spectrum, model category, ABC category
Mathematical Subject Classification 2010
Primary: 19D55
Secondary: 18G55, 55Q91
References
Publication
Received: 23 May 2013
Revised: 2 March 2015
Accepted: 26 April 2015
Published: 6 January 2016
Proposed: Mark Behrens
Seconded: Bill Dwyer, Haynes Miller
Authors
Andrew J Blumberg
Department of Mathematics
The University of Texas
Austin, TX 78712
USA
Michael A Mandell
Department of Mathematics
Indiana University
Rawles Hall
831 E 3rd St
Bloomington, IN 47405
USA