Stable left and right Bousfield localisation

Barnes, D. and Roitzheim, C. (2014) Stable left and right Bousfield localisation. Glasgow Mathematical Journal, 56(1), pp. 13-42. (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 explicitsets 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:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Roitzheim, Dr Constanze
Authors: Barnes, D., and Roitzheim, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Glasgow Mathematical Journal
Publisher:Cambridge University Press
ISSN:0017-0895
ISSN (Online):1469-509X
Copyright Holders:Copyright © 2013 Glasgow Mathematical Journal Trust
First Published:First published in Glasgow Mathematical Journal 56(1):13-42
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
502661Finiteness Structures in Chromatic Derived CategoriesConstanze RoitzheimEngineering & Physical Sciences Research Council (EPSRC)EP/G051348/1M&S - MATHEMATICS