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Homotopical localizations of module spectra


Authors: Carles Casacuberta and Javier J. Gutiérrez
Journal: Trans. Amer. Math. Soc. 357 (2005), 2753-2770
MSC (2000): Primary 55P42, 55P43, 55P60
DOI: https://doi.org/10.1090/S0002-9947-04-03552-4
Published electronically: September 23, 2004
MathSciNet review: 2139526
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Abstract: We prove that stable $f$-localizations (where $f$ is any map of spectra) preserve ring spectrum structures and module spectrum structures, under suitable hypotheses, and we use this fact to describe all possible localizations of the integral Eilenberg-MacLane spectrum $H{\mathbb{Z} }$. As a consequence of this study, we infer that localizations of stable GEMs are stable GEMs, and it also follows that there is a proper class of nonequivalent stable localizations.


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Additional Information

Carles Casacuberta
Affiliation: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
Email: carles.casacuberta@ub.edu

Javier J. Gutiérrez
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain
Address at time of publication: Departament d’Àlgebra i Geometria, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
Email: jgutierr@mat.uab.es, jgutier@mat.ub.es

DOI: https://doi.org/10.1090/S0002-9947-04-03552-4
Keywords: Localization, ring spectrum, module spectrum, stable GEM
Received by editor(s): May 1, 2002
Received by editor(s) in revised form: November 3, 2003
Published electronically: September 23, 2004
Additional Notes: The authors were supported by MCyT grants PB97-0202, BFM2001-2031, and FP98 16587447
Article copyright: © Copyright 2004 American Mathematical Society

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