Volume 16, issue 2 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Localization theorems in topological Hochschild homology and topological cyclic homology

Andrew J Blumberg and Michael A Mandell

Geometry & Topology 16 (2012) 1053–1120

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.

topological Hochschild homology, topological cyclic homology, localization sequence, Mayer–Vietoris sequence, projective bundle theorem, blow-up formula
Mathematical Subject Classification 2010
Primary: 19D55
Secondary: 14F43
Received: 18 November 2010
Revised: 7 February 2012
Accepted: 7 March 2012
Published: 5 June 2012
Proposed: Ralph Cohen
Seconded: Haynes Miller, Jesper Grodal
Andrew J Blumberg
Department of Mathematics
University of Texas at Austin
1 University Station C1200
Austin TX 78712
Michael A Mandell
Department of Mathematics
Indiana University
Rawles Hall
831 E 3rd St
Bloomington IN 47405