Geometry & Topology
- Geom. Topol.
- Volume 16, Number 2 (2012), 1053-1120.
Localization theorems in topological Hochschild homology and topological cyclic homology
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 .
Geom. Topol., Volume 16, Number 2 (2012), 1053-1120.
Received: 18 November 2010
Revised: 7 February 2012
Accepted: 7 March 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
Secondary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Blumberg, Andrew J; Mandell, Michael A. Localization theorems in topological Hochschild homology and topological cyclic homology. Geom. Topol. 16 (2012), no. 2, 1053--1120. doi:10.2140/gt.2012.16.1053. https://projecteuclid.org/euclid.gt/1513732414