An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves
arXiv:1410.4039
Abstract
Orlov's famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. In this paper we show that this result is false without the full faithfulness hypothesis.
55 pages Appendix by Amnon Neeman