Topological André–Quillen cohomology and \(E_{\infty}\) André–Quillen cohomology. (English) Zbl 1027.55009
This paper is concerned with two topological generalisations of André-Quillen cohomology which was originally defined for commutative rings. The first of these generalisations is the André-Quillen cohomology of an \(E_\infty\) simplicial algebra with constant coefficients, and the second is the topological André-Quillen cohomology of an \(E_\infty\) ring spectrum with an Eilenberg-MacLane spectrum as coefficients. In both cases, it is shown that the cohomology is isomorphic to the André-Quillen cohomology of an associated \(E_\infty\) differential graded algebra.
Reviewer: Richard John Steiner (Glasgow)
MSC:
| 55P43 | Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.) |
| 18G55 | Nonabelian homotopical algebra (MSC2010) |
| 13D03 | (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) |
| 18D50 | Operads (MSC2010) |
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