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Abstract: We develop a framework for derived deformation theory, valid in allcharacteristics. This gives a model category reconciling local and globalapproaches to derived moduli theory. In characteristic 0, we use this to showthat the homotopy categories of DGLAs and SHLAs (L infinity algebras)considered by Kontsevich, Hinich and Manetti are equivalent, and are compatiblewith the derived stacks of Toen-Vezzosi and Lurie. Another application is thatthe cohomology groups associated to any classical deformation problem (in anycharacteristic) admit the same operations as Andre-Quillen cohomology.

Author: J. P. Pridham

Source: https://arxiv.org/

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