Homology and Cohomology of E-infinity Ring Spectra

Abstract

Every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andre-Quillen homology or cohomology with appropriate coefficients. Analogous results hold for the category of A-infinity ring spectra and for categories of algebras over many other operads.

References in corpus (1)

• Failure of Brown representability in derived categories

Cited by in corpus (44)

• The tangent complex and Hochschild cohomology of E_n-rings
• Galois extensions of structured ring spectra
• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
• Goodwillie towers and chromatic homotopy: an overview
• Topological Hochschild homology of Thom spectra and the free loop space
• Homotopy theory of modules over operads in symmetric spectra
• Bar constructions and Quillen homology of modules over operads
• Higher topological Hochschild homology of Thom spectra
• Homotopical resolutions associated to deformable adjunctions
• Homotopy completion and topological Quillen homology of structured ring spectra
• Group completion and units in I-spaces
• A general context for Goodwillie Calculus
• Postnikov extensions of ring spectra
• Topological André-Quillen homology for cellular commutative $S$-algebras
• The abstract cotangent complex and Quillen cohomology of enriched categories
• E_n Genera
• Calculating with topological André-Quillen theory, I: Homotopical properties of universal derivations and free commutative $S$-algebras
• Arnold Conjecture and Morava K-theory
• Commutative S-algebras of prime characteristics and applications to unoriented bordism
• Equivariant stable categories for incomplete systems of transfers
• Cubical and cosimplicial descent
• Derived Koszul duality and TQ-homology completion of structured ring spectra
• On the Goodwillie derivatives of the identity in structured ring spectra
• On the derived category of an algebra over an operad
• Generalized Thom spectra and their topological Hochschild homology
• The tangent bundle of a model category
• Fibration theorems for TQ-completion of structured ring spectra
• Infinity-operads and Day convolution in Goodwillie calculus
• Commutative ring spectra
• THH of Thom spectra that are E_\infty ring spectra
• Homotopy theory of modules over operads and non-Sigma operads in monoidal model categories
• On k-invariants for $(\infty ,n)$-categories
• The May-Milgram filtration and $E_k$-cells
• Tangent $\infty$-categories and Goodwillie calculus
• On Deformation Theory in Higher Logarithmic Geometry
• The partition poset complex and the Goodwillie derivatives of the identity in spaces
• Deformations of ${\mathbb{E}}_{\infty }$-groups of units and logarithmic derivatives of ${\mathbb{E}}_{\infty }$-rings
• $E_n$ ring spectra and Dyer-Lashof operations
• Goodwillie calculus in the category of algebras over a chain complex operad
• On the Andre-Quillen homology of Tambara functors
• Topological Quillen localization of structured ring spectra
• (Co)homology of Spectral Categories
• A nilpotent Whitehead theorem for TQ-homology of structured ring spectra