Geometry & Topology 16 (2012) 1053–1120

DOI: 10.2140/gt.2012.16.1053

Abstract

We construct localization cofibration sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of small spectral categories. Using a global construction of the THH and TC 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 K–theory. We also deduce versions of Thomason’s blow-up formula and the projective bundle formula for THH and TC.

Keywords

topological Hochschild homology, topological cyclic homology, localization sequence, Mayer–Vietoris sequence, projective bundle theorem, blow-up formula

Mathematical Subject Classification

Primary: 19D55

Secondary: 14F43

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

Authors