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.
Fourier-Mukai functors in the supported case / A. Canonaco, P. Stellari. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 150:8(2014 Aug), pp. 1349-1383. [10.1112/S0010437X13007872]
Fourier-Mukai functors in the supported case
P. Stellari
2014
Abstract
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.
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