Representability of cohomological functors over extension fields



Rizzardo, Alice ORCID: 0000-0001-8423-6499
(2017) Representability of cohomological functors over extension fields. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 11 (4). pp. 1267-1287.

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Abstract

We generalize a result of Orlov and Van den Bergh on the representability of a cohomological functor from the bounded derived category of a smooth projective variety over a field to the category of L-modules, to the case where L is a field extension of the base field k of the variety X, with L of transcendence degree less than or equal to one or L purely transcendental of degree 2. This result can be applied to investigate the behavior of an exact functor between the bounded derived categories of coherent sheaves of X and Y, with X and Y smooth projective and Y of dimension less than or equal to one or Y a rational surface. We show that for any such F there exists a "generic kernel" A in the derived category of the product, such that F is isomorphic to the Fourier-Mukai transform with kernel A after composing both with the pullback to the generic point of Y.

Item Type: Article
Additional Information: to appear in Journal of Noncommutative Geometry
Uncontrolled Keywords: Representability, base extension, Fourier-Mukai
Depositing User: Symplectic Admin
Date Deposited: 10 Oct 2017 06:47
Last Modified: 11 Dec 2023 13:08
DOI: 10.4171/JNCG/11-4-2
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3009890