Scalar extensions of derived categories and non-Fourier-Mukai functors
arXiv:1402.4506 · doi:10.1016/j.aim.2015.05.013
Abstract
Orlov's famous representability theorem asserts that any fully faithful functor between the derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. This result has been extended by Lunts and Orlov to include functors from perfect complexes to quasi-coherent complexes. In this paper we show that the latter extension is false without the full faithfulness hypothesis. Our results are based on the properties of scalar extensions of derived categories, whose investigation was started by Pawel Sosna and the first author.
arXiv comment35 pages
References in corpus (9)
- Uniqueness of enhancement for triangulated categories
- Sheafifiable homotopy model categories
- Generators and representability of functors in commutative and noncommutative geometry
- Equivalences of derived categories of sheaves on quasi-projective schemes
- Fourier-Mukai functors in the supported case
- Does full imply faithful?
- Scalar extensions of triangulated categories
- On the existence of Fourier-Mukai kernels
- Bimodule complexes via strong homotopy actions