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Fourier–Mukai functors in the supported case

Part of: (Co)homology theory Abelian categories

Published online by Cambridge University Press:  30 June 2014

Alberto Canonaco  and
Paolo Stellari
Alberto Canonaco
Affiliation:
Dipartimento di Matematica ‘F. Casorati’, Università degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy email alberto.canonaco@unipv.it
Paolo Stellari
Affiliation:
Dipartimento di Matematica ‘F. Enriques’, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy email paolo.stellari@unimi.it
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Abstract

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We prove that exact functors between the categories of perfect complexes supported on projective schemes are of Fourier–Mukai type if the functor satisfies a condition weaker than being fully faithful. We also get generalizations of the results in the literature in the case without support conditions. Some applications are discussed and, along the way, we prove that the category of perfect supported complexes has a strongly unique enhancement.

Keywords

derived categoriessupported sheavesFourier–Mukai functors

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 18E10: Exact categories, abelian categories 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 8 , August 2014 , pp. 1349 - 1383
Copyright
© The Author(s) 2014 

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