Topological André--Quillen cohomology and \(E_{\infty}\) André--Quillen cohomology (Q1400952)

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.