Uniqueness of enhancement for triangulated categories

Lunts, Valery; Orlov, Dmitri

doi:10.1090/S0894-0347-10-00664-8

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
DOI: https://doi.org/10.1090/S0894-0347-10-00664-8
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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