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 |
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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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