Uniqueness of enhancement for triangulated categories

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 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.

LATEX, 56 pages. A few minor errors were corrected. Appendix B was added

References in corpus (3)

• Theorie homotopique des DG-categories
• Grothendieck ring of pretriangulated categories
• Equivalences of derived categories of sheaves on quasi-projective schemes

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