# Stable left and right Bousfield localisations

Barnes, David, Roitzheim, Constanze (2014) Stable left and right Bousfield localisations. Glasgow Mathematical Journal, 56 (1). pp. 13-42. ISSN 0017-0895. (doi:10.1017/S0017089512000882)

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## Abstract

We study left and right Bousfield localisations of stable model categories which preserve stability. This follows the lead of the two key examples: localisations of spectra with respect to a homology theory and A-torsion modules over a ring R with A a perfect R-algebra.We exploit stability to see that the resulting model structures are technically far better behaved than the general case.We can give explicit sets of generating cofibrations, show that these localisations preserve properness and give a complete characterisation of when they preserve monoidal structures. We apply these results to obtain convenient assumptions under which a stable model category is spectral. We then use Morita theory to gain an insight into the nature of right localisation and its homotopy category. We finish with a correspondence between left and right localisation.

Item Type: Article 10.1017/S0017089512000882 [UNSPECIFIED] Finiteness structures in chromatic derived categories Model categories, Bousfield localisation, stable homotopy theory Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology > QA612 Algebraic topology Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Constanze Roitzheim 05 Dec 2013 11:46 UTC 29 May 2019 10:01 UTC https://kar.kent.ac.uk/id/eprint/33272 (The current URI for this page, for reference purposes)