A Semi-Orthogonal Decomposition Theorem for Weighted Blowups

TL;DR

This paper generalizes Orlov's classic result by establishing a semi-orthogonal decomposition for weighted blowups of algebraic stacks along Koszul-regular centers, extending the theoretical framework of derived categories.

Contribution

It introduces a semi-orthogonal decomposition for weighted blowups of algebraic stacks, broadening the applicability of Orlov's theorem with a new approach.

Findings

Established a semi-orthogonal decomposition for weighted blowups

Generalized Orlov's result to algebraic stacks with weighted centers

Built on Bergh-Schn"urer's work to extend theoretical understanding

Abstract

We establish a semi-orthogonal decomposition for the weighted blowup of an algebraic stack along a Koszul-regular weighted centre, generalising the classic result of Orlov. Our approach is based on the work of Bergh-Schn\"urer.