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Homotopy theory of modules over diagrams of rings
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Greenlees, John and Shipley, B. E. (2014) Homotopy theory of modules over diagrams of rings. Proceedings of the AMS Series B, 1 . pp. 89-104. doi:10.1090/S2330-1511-2014-00012-2 ISSN 2330-1511.
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Official URL: https://doi.org/10.1090/S2330-1511-2014-00012-2
Abstract
Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we consider the category of diagrams where the object X(s) at s comes from M(s). We develop model structures on such categories of diagrams, and Quillen adjunctions that relate categories based on different diagram shapes. Under certain conditions, cellularizations (or right Bousfield localizations) of these adjunctions induce Quillen equivalences. As an application we show that a cellularization of a category of modules over a diagram of ring spectra (or differential graded rings) is Quillen equivalent to modules over the associated inverse limit of the rings. Another application of the general machinery here is given in work by the authors on algebraic models of rational equivariant spectra. Some of this material originally appeared in the preprint “An algebraic model for rational torus-equivariant stable homotopy theory”, arXiv:1101.2511, but has been generalized here.
Item Type: | Journal Article | |||||||||
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Subjects: | Q Science > QA Mathematics | |||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
Library of Congress Subject Headings (LCSH): | Homotopy theory, Adjunction theory | |||||||||
Journal or Publication Title: | Proceedings of the AMS Series B | |||||||||
Publisher: | American Mathematical Society | |||||||||
ISSN: | 2330-1511 | |||||||||
Official Date: | 3 September 2014 | |||||||||
Dates: |
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Volume: | 1 | |||||||||
Page Range: | pp. 89-104 | |||||||||
DOI: | 10.1090/S2330-1511-2014-00012-2 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Description: | MathSciNet review: 3254575 |
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Date of first compliant deposit: | 20 March 2018 | |||||||||
Date of first compliant Open Access: | 22 March 2018 | |||||||||
RIOXX Funder/Project Grant: |
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