Equivalences of derived categories of sheaves on quasi-projective schemes

TL;DR

This paper extends Orlov's results on the equivalence of derived categories of sheaves to quasi-projective schemes, broadening the understanding of their categorical relationships.

Contribution

It generalizes Orlov's representability theorem from projective to quasi-projective schemes, providing new insights into derived category equivalences.

Findings

Extended Orlov's theorem to quasi-projective schemes

Established conditions for derived equivalences in broader settings

Enhanced understanding of categorical relationships in algebraic geometry

Abstract

We extend Orlov's result on representability of equivalences to schemes projective over a field. We also investigate the quasi-projective case.