Abstract
Starting from a sheaf of associative algebras over a scheme we show thatits deformation theory is described by cohomologies of a canonical object,called the cotangent complex, in the derived category of sheaves ofbi-modules over this sheaf of algebras. The passage from deformations tocohomology is based on considering a site which is naturally constructed outof our sheaf of algebras. It turns out that on the one hand, cohomology ofcertain sheaves on this site control deformations, and on the other hand,they can be rewritten in terms of the category of sheaves of bi-modules.
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GAITSGORY, D. Grothendieck topologies and deformation Theory II. Compositio Mathematica 106, 321–348 (1997). https://doi.org/10.1023/A:1000129507602
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DOI: https://doi.org/10.1023/A:1000129507602