STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS
Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 13-42
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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.
BARNES, DAVID; ROITZHEIM, CONSTANZE. STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS. Glasgow mathematical journal, Tome 56 (2014) no. 1, pp. 13-42. doi: 10.1017/S0017089512000882
@article{10_1017_S0017089512000882,
author = {BARNES, DAVID and ROITZHEIM, CONSTANZE},
title = {STABLE {LEFT} {AND} {RIGHT} {BOUSFIELD} {LOCALISATIONS}},
journal = {Glasgow mathematical journal},
pages = {13--42},
year = {2014},
volume = {56},
number = {1},
doi = {10.1017/S0017089512000882},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000882/}
}
TY - JOUR AU - BARNES, DAVID AU - ROITZHEIM, CONSTANZE TI - STABLE LEFT AND RIGHT BOUSFIELD LOCALISATIONS JO - Glasgow mathematical journal PY - 2014 SP - 13 EP - 42 VL - 56 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000882/ DO - 10.1017/S0017089512000882 ID - 10_1017_S0017089512000882 ER -
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