Localization theorems in topological Hochschild homology and topological cyclic homology

Details Localization theorems in topological Hochschild homology and topological cyclic homology Localization theorems in topological Hochschild homology and topological cyclic homology

2008-02-27

arxiv.org/abs/0802.3938v3

Mathematics

K-Theory and Homology

Added an appendix on the cyclotomic structure map

Scientific paper

We construct localization cofiber sequences for the topological Hochschild homology (THH) and topological cyclic homology (TC) of 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 cofiber 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.

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