Volume 10, issue 1 (2010)

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

Volume 21, 1 issue

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
Generalized spectral categories, topological Hochschild homology and trace maps

Gonçalo Tabuada

Algebraic & Geometric Topology 10 (2010) 137–213

Given a monoidal model category C and an object K in C, Hovey constructed the monoidal model category SpΣ(C,K) of K–symmetric spectra over C. In this paper we describe how to lift a model structure on the category of C–enriched categories to the category of SpΣ(C,K)–enriched categories. This allow us to construct a (four step) zig-zag of Quillen equivalences comparing dg categories to H–categories. As an application we obtain: (1) the invariance under weak equivalences of the topological Hochschild homology (THH) and topological cyclic homology (TC) of dg categories; (2) non-trivial natural transformations from algebraic K–theory to THH.

symmetric spectra, Eilenberg–Mac Lane spectra, spectral categories, Dg categories, Quillen model structure, Bousfield localization, topological Hochschild homology, topological cyclic homology, trace maps
Mathematical Subject Classification 2000
Primary: 55P42, 18D20, 18G55
Secondary: 19D55
Received: 18 September 2008
Revised: 28 July 2009
Accepted: 15 October 2009
Published: 10 January 2010
Gonçalo Tabuada
Departamento de Matemática e CMA
Quinta da Torre
2829-516 Caparica