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Localization theorems in
topological Hochschild homology and topological cyclic
homology
Andrew J Blumberg and Michael A Mandell |
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Geometry & Topology 16 (2012) 1053–1120
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Abstract |
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We construct localization cofibration sequences for the topological Hochschild homology () and topological cyclic homology () of small spectral categories. Using a global construction of the and of a scheme in terms of the perfect complexes in a spectrally enriched version of the category of unbounded complexes, the sequences specialize to localization cofibration sequences associated to the inclusion of an open subscheme. These are the targets of the cyclotomic trace from the localization sequence of Thomason–Trobaugh in –theory. We also deduce versions of Thomason’s blow-up formula and the projective bundle formula for and . |
Keywords
topological Hochschild homology, topological cyclic
homology, localization sequence, Mayer–Vietoris sequence,
projective bundle theorem, blow-up formula
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Mathematical Subject Classification 2010
Primary: 19D55
Secondary: 14F43
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References |
Publication
Received: 18 November 2010
Revised: 7 February 2012
Accepted: 7 March 2012
Published: 5 June 2012
Proposed: Ralph Cohen
Seconded: Haynes Miller, Jesper Grodal
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Authors |
| Andrew J Blumberg | |
| Department of Mathematics University of Texas at Austin 1 University Station C1200 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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