Euivalences of derived catgories of sheaves on smooth stacks

TL;DR

This paper extends Orlov's theorem to establish equivalences of derived categories of sheaves on smooth stacks related to normal projective varieties with quotient singularities.

Contribution

It generalizes the representability theorem to smooth stacks arising from varieties with quotient singularities.

Findings

Derived categories of sheaves on these stacks are equivalent under certain conditions.

The extension broadens the applicability of Orlov's theorem to singular varieties.

Provides new tools for studying sheaves on algebraic stacks.

Abstract

We extend Orlov's representability theorem on the equivalence of derived categories of sheaves to the case of smooth stacks associated to normal projective varieties with only quotient singularities.