HZ -algebra spectra are differential graded algebras

By B. Shipley. 2002

214 citations recorded by the source corpus.

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 basically any rational stable model category is Quillen equivalent to modules over a differential graded Q-algebra (with many objects).

Subfields: Geometry and Topology, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/819f849bbc31b5992fa0e25348beb98b6f2f496a

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Fernando Muro
2. B. Keller
3. I. Reiten
4. Pierre-Guy Plamondon
5. Osamu Iyama
6. Bernard Leclerc
7. Alexander Kuznetsov
8. Ralf Schiffler

In Mathematical Physics

1. Fernando Muro
2. B. Keller
3. Alexander Kuznetsov
4. I. Reiten
5. Osamu Iyama
6. Bin Zhu
7. Pierre-Guy Plamondon
8. Amnon Yekutieli

In Molecular Biology

1. Fernando Muro
2. B. Keller

Citations in the corpus

• Dwyer–Kan homotopy theory of enriched categories (2012, methodology): “S. Schwede and B. Shipley, ‘Equivalences of monoidal model categories’, Algebr.”
• Integral Transforms and Drinfeld Centers in Derived Algebraic Geometry (2008, unknown): “(See [ Sh ] and references therein for the relation of algebra over rings and over the corresponding Eilernberg-MacLane spectra.)”
• On differential graded categories (2006, background): “The explicit description of the two algebras is given in [140], [36], [38].”