Fourier-Mukai functors in the supported case

Details Fourier-Mukai functors in the supported case Fourier-Mukai functors in the supported case

2010-10-05

arxiv.org/abs/1010.0798v2

Mathematics

Algebraic Geometry

32 pages. Major revision and new results added

Scientific paper

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 non-supported case. 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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