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2014 Commutative ring objects in pro-categories and generalized Moore spectra
Daniel G Davis, Tyler Lawson
Geom. Topol. 18(1): 103-140 (2014). DOI: 10.2140/gt.2014.18.103

Abstract

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 This is applied to obtain an unpublished result of M J Hopkins that certain towers of generalized Moore spectra, closely related to the K(n)–local sphere, are E–algebras in the category of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.

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Daniel G Davis. Tyler Lawson. "Commutative ring objects in pro-categories and generalized Moore spectra." Geom. Topol. 18 (1) 103 - 140, 2014. https://doi.org/10.2140/gt.2014.18.103

Information

Received: 22 August 2012; Revised: 7 April 2013; Accepted: 13 June 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1339.55011
MathSciNet: MR3158773
Digital Object Identifier: 10.2140/gt.2014.18.103

Subjects:
Primary: 55P43, 55U35
Secondary: 18D20, 18D50, 18G55

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.18 • No. 1 • 2014
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