Fully faithfulness criteria for quasi-projective schemes

Abstract

We extend to quasi-projective schemes that kind of Bondal-Orlov’s criterion for a Fourier-Mukai functor to be fully faithful and we prove a variant of it valid in arbitrary characteristic. As a first application of these criteria we prove the fully faithfulness of the Fourier-Mukai functor used to show the autoduality of the compactified Jacobian for reduced projective curves with locally planar singularities.