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Deformation theory of objects in homotopy and derived categories I: General theory |
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| Authors: | Alexander I Efimov Valery A Lunts Dmitri O Orlov |
| Institution: | a Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia b Independent University of Moscow, Moscow, Russia c Department of Mathematics, Indiana University, Bloomington, IN 47405, USA d Algebra Section, Steklov Mathematical Institute, 8 Gubkina str., Moscow, 119991, Russia |
| Abstract: | 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 Defh(E), coDefh(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. |
| Keywords: | Derived categories Differential graded categories Moduli spaces Deformation theory Noncommutative geometry |
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