New examples of non-Fourier-Mukai functors

Abstract

A celebrated result by Orlov states that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of geometric origin, i.e. it is a Fourier-Mukai functor. In this paper we prove that any smooth projective variety of dimension ≥ 3 equipped with a tilting bundle can serve as the source variety of a non-Fourier-Mukai functor between smooth projective schemes.