Lazarev: Cohomology theories for highly structured ring spectra
arXiv: Experimental full text search
BN, AT (Algebraic topology)?
Toen and Vezzosi: Algebraic geometry over model categories. Early paper, looks very nice! Applications to interpreting DG-schemes, and to defining etale K-theory of E-infty algebras. Expectation to extend the classical work for E-infty algebras to the more general setting of AG over a model cat, for the following concepts: tangent Lie algebra, cotangent complex, Hochschild cohom, K-theory, A-Q cohomology. Would like to do AG over a symmetric monoidal infty-cat, need strictification results. An E-infty alg should be a monoid in a SM infty-cat. Pp 34: Short nice review of operads and E-infty stuff.
arXiv:1208.1868 Calculating with topological André-Quillen theory, I: Homotopical properties of universal derivations and free commutative -algebras from arXiv Front: math.AT by Andrew Baker We adopt the viewpoint that topological Andé-Quillen theory for commutative -algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on homotopical properties of universal derivations, especially their behaviour in multiplicative homology theories. There are algebraic derivation properties, but also deeper properties arising from the homotopical structure of the free algebra construction and its relationship with extended powers of spectra. In the connective case in ordinary homology, this leads to useful formulae involving Dyer-Lashof operations in the homology of commutative -algebras. Although some of our results should be obtainable using stabilisation, our approach seems more direct. We also discuss a reduced free algebra construction .
nLab page on Topological Andre-Quillen cohomology