Scalar extensions of derived categories and non-Fourier-Mukai functors



Rizzardo, Alice ORCID: 0000-0001-8423-6499 and Van den Bergh, Michel
(2015) Scalar extensions of derived categories and non-Fourier-Mukai functors. ADVANCES IN MATHEMATICS, 281. 1100 - 1144.

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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. 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.

Item Type: Article
Uncontrolled Keywords: Fourier-Mukai functor, Orlov's theorem
Depositing User: Symplectic Admin
Date Deposited: 19 Dec 2017 09:32
Last Modified: 16 Apr 2021 11:43
DOI: 10.1016/j.aim.2015.05.013
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3014473