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2 results

  • Uniqueness of enhancements for derived and geometric categories

  • Part of
  • Alberto Canonaco, Amnon Neeman, Paolo Stellari
  • Journal:
    Forum of Mathematics, Sigma / Volume 10 / 2022
    Published online by Cambridge University Press:
    20 October 2022, e92
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  • We prove that the derived categories of abelian categories have unique enhancements—all of them, the unbounded, bounded, bounded above and bounded below derived categories. The unseparated and left completed derived categories of a Grothendieck abelian category are also shown to have unique enhancements. Finally, we show that the derived category of complexes with quasi-coherent cohomology and the category of perfect complexes have unique enhancements for quasi-compact and quasi-separated schemes.

  • Fourier–Mukai functors in the supported case

  • Part of
  • Alberto Canonaco, Paolo Stellari
  • Journal:
    Compositio Mathematica / Volume 150 / Issue 8 / August 2014
    Published online by Cambridge University Press:
    30 June 2014, pp. 1349-1383
    Print publication:
    August 2014
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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.