HZ-algebra spectra are differential graded algebras

2002/09/17 by Brooke Shipley, Shipley, Brooke · 4 citations
Mathematics · #18G35 #55P43 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0209215

openalex publication_date 2002/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZ-algebra spectra. We also construct Quillen equivalences between the differential graded modules and module spectra over these algebras. We use these equivalences in turn to produce algebraic models for rational stable model categories. We show that bascially any rational stable model category is Quillen equivalent to modules over a differential graded Q-algebra (with many objects).

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