An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves



Rizzardo, Alice ORCID: 0000-0001-8423-6499, Van den Bergh, Michel and Neeman, Amnon
(2019) An example of a non-Fourier-Mukai functor between derived categories of coherent sheaves. Inventiones Mathematicae, 216. 927 - 1004.

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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. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homotopy category of spectral categories if the ground field is \({\mathbb Q}\).

Item Type: Article
Additional Information: 55 pages
Uncontrolled Keywords: math.AG, math.AG, 13D09, 18E30, 14A22
Depositing User: Symplectic Admin
Date Deposited: 21 Jan 2019 09:17
Last Modified: 16 Apr 2021 11:43
DOI: 10.1007/s00222-019-00862-9
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3031571