Mathematics – Algebraic Geometry
Scientific paper
2007-02-27
Adv. Math. 222 (2009), no. 2, 359--401
Mathematics
Algebraic Geometry
Alexander Efimov is a new co-author of this paper. Besides some minor changes, Proposition 7.1 and Theorem 8.1 were corrected
Scientific paper
This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module $E$ over a DG category we define four deformation functors $\Def ^{\h}(E)$, $\coDef ^{\h}(E)$, $\Def (E)$, $\coDef (E)$. The first two functors describe the deformations (and co-deformations) of $E$ in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras.
Efimov Alexander I.
Lunts Valery A.
Orlov Dmitri O.
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