Orlov's Theorem in the Smooth Proper Case

TL;DR

This paper extends Orlov's theorem, showing that certain functors between derived categories of smooth proper varieties are Fourier--Mukai transforms, broadening the class of varieties where this equivalence holds.

Contribution

The work generalizes Orlov's result from smooth projective to smooth proper varieties, establishing Fourier--Mukai equivalences in a broader geometric context.

Findings

Proves that certain functors are Fourier--Mukai transforms for smooth proper varieties.

Extends the class of varieties where derived category functors are representable.

Provides new tools for understanding derived equivalences in algebraic geometry.

Abstract

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.