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The
homotopy theory of cyclotomic spectra
Andrew J Blumberg and Michael A Mandell |
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Geometry & Topology 19 (2015) 3105–3147
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Abstract |
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We describe spectral model category structures on the categories of cyclotomic spectra and –cyclotomic spectra (in orthogonal spectra) with triangulated homotopy categories. We show that the functors and 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 and the derived mapping spectrum out of the sphere spectrum in the category of –cyclotomic spectra corepresents the –completion of . |
Keywords
topological cyclic homology, cyclotomic spectrum, model
category, ABC category
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Mathematical Subject Classification 2010
Primary: 19D55
Secondary: 18G55, 55Q91
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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
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Authors |
| Andrew J Blumberg | |
| Department of Mathematics The University of Texas Austin, TX 78712 USA |
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| Michael A Mandell | |
| Department of Mathematics Indiana University Rawles Hall 831 E 3rd St Bloomington, IN 47405 USA |
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