Deformation theory of objects in homotopy and derived categories I: General theory

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...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2009-10, Vol.222 (2), p.359-401
Main Authors: Efimov, Alexander I., Lunts, Valery A., Orlov, Dmitri O.
Format: Article
Language:English
Subjects:
Deformation theory
Derived categories
Differential graded categories
Moduli spaces
Noncommutative geometry
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2009.03.021