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.
Keywords
Cite
@article{arxiv.0908.4187,
title = {Uniqueness of enhancement for triangulated categories},
author = {Valery A. Lunts and Dmitri O. Orlov},
journal= {arXiv preprint arXiv:0908.4187},
year = {2012}
}
Comments
LATEX, 56 pages. A few minor errors were corrected. Appendix B was added