Topological AndreQuillen cohomology

General Introduction
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Search results
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Online References
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Toen and Vezzosi: Algebraic geometry over model categories. Early paper, looks very nice! Applications to interpreting DGschemes, and to defining etale Ktheory of Einfty algebras. Expectation to extend the classical work for Einfty algebras to the more general setting of AG over a model cat, for the following concepts: tangent Lie algebra, cotangent complex, Hochschild cohomology, Ktheory, AQ cohomology. Would like to do AG over a symmetric monoidal inftycat, need strictification results. An Einfty alg should be a monoid in a SM inftycat. Pp 34: Short nice review of operads and Einfty stuff.
arXiv:1208.1868 Calculating with topological AndréQuillen theory, I: Homotopical properties of universal derivations and free commutative $S$algebras from arXiv Front: math.AT by Andrew Baker We adopt the viewpoint that topological AndéQuillen theory for commutative $S$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 $\mathbb{P}R$ and its relationship with extended powers of spectra. In the connective case in ordinary $\bmod{p}$ homology, this leads to useful formulae involving DyerLashof operations in the homology of commutative $S$algebras. Although some of our results should be obtainable using stabilisation, our approach seems more direct. We also discuss a reduced free algebra construction $\tilde{\mathbb{P}}R$.
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