Commutative ring objects in pro-categories and generalized Moore spectra

Daniel G. Davis, Tyler Lawson

Research output: Contribution to journalArticle

1 Scopus citations

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 This is applied to obtain an unpublished result of MJ Hopkins that certain towers of generalized Moore spectra, closely related to the K.n/-local sphere, are E-algebras in the category of pro-spectra.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.

Original languageEnglish (US)
Pages (from-to)103-140
Number of pages38
JournalGeometry and Topology
Volume18
Issue number1
DOIs
StatePublished - Nov 21 2013

Keywords

  • Endomorphism operad
  • Moore spectra
  • Pro-objects
  • Structured ring spectra

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