Unifying derived deformation theories
By J. Pridham. 2007
190 citations recorded by the source corpus.
Abstract We develop a framework for derived deformation theory, valid in all characteristics. This gives a model category reconciling local and global approaches to derived moduli theory. In characteristic 0, we use this to show that the homotopy categories of DGLAs and SHLAs ( L ∞ -algebras) considered by Kontsevich, Hinich and Manetti are equivalent, and are compatible with the derived stacks of Toen–Vezzosi and Lurie. Another application is that the cohomology groups associated to any classical deformation problem (in any characteristic) admit the same operations as Andre–Quillen cohomology.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a4fc58273185aaa8c383ca66a018bad536d3cdcc
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Presenting higher stacks as simplicial schemes (2013, background): “model the corresponding n-geometric stacks. For an infinitesimal version, we could take Ato be the category of left-exact set-valued functors on Artinian simplicial rings (so A= cSp in the notation of [Pri2]), and C the class of formally smooth morphisms. Then the key notions in [Pri2] of quasi-smoot”