English

Fourier-Mukai functors in the supported case

Algebraic Geometry 2014-07-09 v3

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.

Keywords

Cite

@article{arxiv.1010.0798,
  title  = {Fourier-Mukai functors in the supported case},
  author = {Alberto Canonaco and Paolo Stellari},
  journal= {arXiv preprint arXiv:1010.0798},
  year   = {2014}
}

Comments

36 pages. Major revision and new results added. Accepted for publication in Compositio Math

R2 v1 2026-06-21T16:23:50.938Z