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Commutative ring objects
in pro-categories and generalized Moore spectra
Daniel G Davis and Tyler Lawson |
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Geometry & Topology 18 (2014) 103–140
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Abstract |
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We develop a rigidity criterion to show that in simplicial model categories with a compatible symmetric monoidal structure, operad structures can be automatically lifted along certain maps. This is applied to obtain an unpublished result of M J Hopkins that certain towers of generalized Moore spectra, closely related to the –local sphere, are –algebras in the category of pro-spectra. In addition, we show that Adams resolutions automatically satisfy the above rigidity criterion. In order to carry this out we develop the concept of an operadic model category, whose objects have homotopically tractable endomorphism operads. |
Keywords
Moore spectra, pro-objects, structured ring spectra,
endomorphism operad
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Mathematical Subject Classification 2010
Primary: 55P43, 55U35
Secondary: 18D20, 18D50, 18G55
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References |
Publication
Received: 22 August 2012
Revised: 7 April 2013
Accepted: 13 June 2013
Preview posted: 21 November 2013
Published: 9 January 2014
Proposed: Bill Dwyer
Seconded: Haynes Miller, Paul Goerss
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Authors |
| Daniel G Davis | |
| Department of Mathematics University of Louisiana at Lafayette 1403 Johnston Street Maxim Doucet Hall, Room 217 Lafayette, LA 70504-1010, USA |
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| http://www.ucs.louisiana.edu/~dxd0799/ | |
| Tyler Lawson | |
| Department of Mathematics University of Minnesota 206 Church St SE Minneapolis, MN 55455, USA |
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| http://math.umn.edu/~tlawson/ | |
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