Bondal-Orlov's reconstruction theorem in noncommutative projective geometry

TL;DR

This paper extends Bondal-Orlov's reconstruction theorem to noncommutative projective geometry and demonstrates that certain functors are of Fourier-Mukai type, advancing the understanding of derived categories in noncommutative settings.

Contribution

It generalizes a key reconstruction theorem to noncommutative geometry and characterizes functors as Fourier-Mukai, providing new tools for noncommutative algebraic geometry.

Findings

Reconstruction theorem holds in noncommutative projective geometry.

Fully faithful exact functors are of Fourier-Mukai type.

Advances understanding of derived categories in noncommutative contexts.

Abstract

We show that Bondal-Orlov's reconstruction theorem holds in noncommutative projective geometry. We also prove that fully faithful exact functors between derived categories of noncommutative projective schemes are of Fourier-Mukai type.