New examples of non-Fourier-Mukai functors

TL;DR

This paper demonstrates that for smooth projective varieties of dimension three or higher with a tilting bundle, there exist non-Fourier-Mukai functors connecting them to other smooth projective schemes, expanding the understanding of derived functors.

Contribution

It introduces the existence of non-Fourier-Mukai functors from certain high-dimensional varieties with tilting bundles, a novel class of derived functors in algebraic geometry.

Findings

Existence of non-Fourier-Mukai functors for varieties with tilting bundles.

Construction of explicit examples in dimensions ≥ 3.

Extends the class of known derived functors beyond Fourier-Mukai type.

Abstract

In this paper we prove that any smooth projective variety of dimension $\ge 3$ equipped with a tilting bundle can serve as the source variety of a non-Fourier-Mukai functor between smooth projective schemes.