On localizing subcategories of derived categories of categories of quasi-coherent sheaves on Noetherian algebraic spaces

TL;DR

This paper characterizes localizing subcategories of derived categories of quasi-coherent sheaves on Noetherian algebraic spaces using subsets of their underlying topological spaces, providing a geometric perspective.

Contribution

It offers a new interpretation of localizing subcategories in derived categories of algebraic spaces through topological subsets, extending previous results from schemes to algebraic spaces.

Findings

Localizing subcategories correspond to subsets of the underlying space

Provides a geometric classification of subcategories

Extends known results from schemes to algebraic spaces

Abstract

Let $S$ be a scheme contained in $\mathbf{Sch}_{fppf}$. Let $\mathfrak{X}$ be a Noetherian separated algebraic space over $S$. In this paper, we interpret localizing subcategories of the derived category of $\mathfrak{X}$ by using subsets of $|\mathfrak{X}|$.