Generalized spectral categories, topological Hochschild homology and trace maps

Tabuada, Gonçalo¹

¹Departamento de Matemática e CMA, FCT-UNL, Quinta da Torre, 2829-516 Caparica, Portugal

Algebraic and Geometric Topology, Tome 10 (2010) no. 1, pp. 137-213

Résumé

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 Hℤ–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.

Détail

DOI : 10.2140/agt.2010.10.137

Keywords: symmetric spectra, Eilenberg–Mac Lane spectra, spectral categories, Dg categories, Quillen model structure, Bousfield localization, topological Hochschild homology, topological cyclic homology, trace maps

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