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Fourier–Mukai functors in the supported case

Published online by Cambridge University Press:  30 June 2014

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.

Type
Research Article
Copyright
© The Author(s) 2014 

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