Homology and cohomology of E∞ ring spectra

By M. Basterra, Michael A. Mandell. 2004

90 citations recorded by the source corpus.

Abstract.Every homology or cohomology theory on a category of E∞ ring spectra is Topological André–Quillen homology or cohomology with appropriate coefficients. Analogous results hold more generally for categories of algebras over operads.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/778513a806dc0c93995e1e9acd080fa6d822e11e

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In Algebra and Number Theory

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Citations in the corpus

Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory (2014, unknown): “(See also [ 4 , § 6] for discussion of this adjunction.)”
The tangent complex and Hochschild cohomology of $\mathcal {E}_n$-rings (2011, unknown): “ivalence Stab(O-alg(C)/A) ≃ModO A(C) and equivalences of functors Σ∞ ∗ ≃L A and Ω∞ ≃A⊕(−). Remark 2.18. An equivalent result, in the case where Cis spectra, was previously provedby BasterraMandell in [BM1]. We will require the following lemma from the Goodwillie calculus, which is a familiar fact co”
Topological Hochschild homology of Thom spectra and the free loop space (2008, background): “(This construction models the tensor of Z with finite based sets in the category of augmented commutative monoids in A; similar constructions are considered in [4] and [37].”
Goodwillie towers and chromatic homotopy: an overview (2004, methodology): “D/ in the ‘usual way’: this has been studied carefully by Schwede [43] (following Bousfield–Friedlander [10]), Hovey [21], and Basterra–Mandell [5].”
Homotopy theory of modules over operads in symmetric spectra (2007, background): “1 Introduction Operads parametrize simple and complicated algebraic structures and naturally arise in several areas of algebraic topology, homotopy theory and homological algebra; see Basterra and Mandell [1], Goerss and Hopkins [13], Hinich and Schechtman [18], Kriz and May [24], May [30] and McClu”
Model Categories and Simplicial Methods (2006, background): “André-Quillen (co-)homology arises naturally in homotopy theoretic settings: see for example, [1], [4], [18], and [19].”