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Grothendieck topologies and deformation Theory II

Published online by Cambridge University Press:  04 December 2007

D. GAITSGORY
D. GAITSGORY
Affiliation:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv, Israel; e-mail address: gaitsgde@math.tau.ac.il
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Abstract

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Starting from a sheaf of associative algebras over a scheme we show that its deformation theory is described by cohomologies of a canonical object, called the cotangent complex, in the derived category of sheaves of bi-modules over this sheaf of algebras. The passage from deformations to cohomology is based on considering a site which is naturally constructed out of our sheaf of algebras. It turns out that on the one hand, cohomology of certain 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.

Keywords

Grothendieck topologiessheavesdeformationsderived categories
Type
Research Article
Information
Compositio Mathematica , Volume 106 , Issue 3 , May 1997 , pp. 321 - 348
Copyright
© 1997 Kluwer Academic Publishers