Unifying derived deformation theories

Details Unifying derived deformation theories Unifying derived deformation theories

2007-05-02

arxiv.org/abs/0705.0344v6

Adv. Math. 224 (2010), no.3, 772-826

Mathematics

Algebraic Geometry

55 pages; v4 split in two - other half is now arXiv:0908.1963; v5 final version, to appear in Adv. Math; v6 incorporates conte

Scientific paper

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 infinity 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.

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