Book contents
- Frontmatter
- Contents
- Preface
- The development of structured ring spectra
- Compromises forced by Lewis's theorem
- Permutative categories as a model of connective stable homotopy
- Morita theory in abelian, derived and stable model categories
- Higher coherences for equivariant K-theory
- (Co-)Homology theories for commutative (S-)algebras
- Classical obstructions and S-algebras
- Moduli spaces of commutative ring spectra
- Cohomology theories for highly structured ring spectra
- Index
Moduli spaces of commutative ring spectra
Published online by Cambridge University Press: 23 October 2009
- Frontmatter
- Contents
- Preface
- The development of structured ring spectra
- Compromises forced by Lewis's theorem
- Permutative categories as a model of connective stable homotopy
- Morita theory in abelian, derived and stable model categories
- Higher coherences for equivariant K-theory
- (Co-)Homology theories for commutative (S-)algebras
- Classical obstructions and S-algebras
- Moduli spaces of commutative ring spectra
- Cohomology theories for highly structured ring spectra
- Index
Summary
Abstract. Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E ∗E is flat over E∗. We wish to address the following question: given a commutative E∗-algebra A in E∗E-comodules, is there an E∞-ring spectrum X with E∗X ≅ A as comodule algebras? We will formulate this as a moduli problem, and give a way – suggested by work of Dwyer, Kan, and Stover – of dissecting the resulting moduli space as a tower with layers governed by appropriate André-Quillen cohomology groups. A special case is A = E∗E itself. The final section applies this to discuss the Lubin-Tate or Morava spectra En.
Some years ago, Alan Robinson developed an obstruction theory based on Hochschild cohomology to decide whether or not a homotopy associative ring spectrum actually has the homotopy type of an A∞-ring spectrum. In his original paper on the subject [35] he used this technique to show that the Morava K-theory spectra K(n) can be realized as an A∞-ring spectrum; subsequently, in [3], Andrew Baker used these techniques to show that a completed version of the Johnson-Wilson spectrum E(n) can also be given such a structure. Then, in the mid-90s, the second author and Haynes Miller showed that the entire theory of universal deformations offinite height formal group laws over fields of non-zero characteristic can be lifted to A∞-ring spectra in an essentially unique way.
- Type
- Chapter
- Information
- Structured Ring Spectra , pp. 151 - 200Publisher: Cambridge University PressPrint publication year: 2004
- 87
- Cited by