Mathematics – Algebraic Geometry
Scientific paper
2009-08-28
J. Amer. Math. Soc. 23 (2010), 3, 853--908
Mathematics
Algebraic Geometry
LATEX, 56 pages. A few minor errors were corrected. Appendix B was added
Scientific paper
10.1090/S0894-0347-10-00664-8
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 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.
Lunts Valery A.
Orlov Dmitri O.
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