@TECHREPORT{Goerss99simplicialstructured, author = {P. G. Goerss and M. J. Hopkins}, title = {Simplicial Structured Ring Spectra}, institution = {}, year = {1999} }

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Abstract

We examine the foundations of simplicial algebras in spectra over a simplicial operad. We are led to simplicial operads and simplicial algebras over simplicial operads because certain operads which are notoriously hard to work with { mainly the E1 operad { can be simplicially resolved by simpler pieces. Our main goals are to a build spectral sequence for computing spaces of maps between structured ring spectra, and to develop a Dwyer-Kan-Stover style obstruction theory for deciding when a spectrum actually can be a structured ring spectrum. In this paper we work out some of the foundations of the homotopy theory of simplicial ring spectra over a simplicial operad. This is not a gratuitous act of generalization. Simplicial objects in any category are a standard mechanism for building the resolutions necessary for computations; this is how simplicial spectra arise. The simplicial operads arise as an answer to an immediate practical problem. If T is an E1 operad over the linear isometrie...