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Uniqueness of enhancement for triangulated categories

Authors: Valery A. Lunts and Dmitri O. Orlov
Journal: J. Amer. Math. Soc. 23 (2010), 853-908
MSC (2010): Primary 14F05, 18E30
Published electronically: February 8, 2010
MathSciNet review: 2629991
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Abstract: The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such uniqueness for the unbounded derived categories of quasi-coherent sheaves, for the triangulated categories of perfect complexes, and for the bounded derived categories of coherent sheaves on quasi-projective schemes. If a scheme is projective, then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded derived categories of coherent sheaves. These results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product.

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Additional Information

Valery A. Lunts
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

Dmitri O. Orlov
Affiliation: Steklov Mathematical Institute, 8 Gubkina St., Moscow, Russia

Keywords: Triangulated categories, DG categories, derived categories of sheaves
Received by editor(s): September 5, 2009
Received by editor(s) in revised form: December 14, 2009
Published electronically: February 8, 2010
Additional Notes: The first author was partially supported by the NSA grant H98230-05-1-0050
The second author was partially supported by grant RFFI 08-01-00297 and grant NSh-1987.2008.1
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.