Holmstrom Topological Andre-Quillen cohomology

Topological Andre-Quillen cohomology

Lazarev: Cohomology theories for highly structured ring spectra


Topological Andre-Quillen cohomology

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Topological Andre-Quillen cohomology

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Topological Andre-Quillen cohomology

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 SS-algebras from arXiv Front: math.AT by Andrew Baker We adopt the viewpoint that topological Andé-Quillen theory for commutative SS-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 R\mathbb{P}_R and its relationship with extended powers of spectra. In the connective case in ordinary bmodp\bmod{p} homology, this leads to useful formulae involving Dyer-Lashof operations in the homology of commutative SS-algebras. Although some of our results should be obtainable using stabilisation, our approach seems more direct. We also discuss a reduced free algebra construction ˜ R\tilde{\mathbb{P}}_R.

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Created on June 10, 2014 at 21:14:54 by Andreas Holmström