Twisted Fourier-Mukai functors

Details Twisted Fourier-Mukai functors Twisted Fourier-Mukai functors

2006-05-09

arxiv.org/abs/math/0605229v2

Mathematics

Algebraic Geometry

16 pages. Minor changes. Final version to appear in Adv. Math

Scientific paper

Due to a theorem by Orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of Fourier-Mukai type. We extend this result to the case of bounded derived categories of twisted coherent sheaves and at the same time we weaken the hypotheses on the functor. As an application we get a complete description of the exact functors between the abelian categories of twisted coherent sheaves on smooth projective varieties.

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