Absolute noetherian approximation of algebraic stacks

TL;DR

This paper demonstrates that any quasi-compact, quasi-separated algebraic stack can be approximated by a noetherian algebraic stack, enabling broader applications in the theory of moduli spaces.

Contribution

It introduces a method to approximate non-noetherian algebraic stacks with noetherian ones, expanding the toolkit for algebraic geometry.

Findings

Every quasi-compact, quasi-separated algebraic stack can be approximated by a noetherian algebraic stack

Applications include removing noetherian assumptions in the theory of good moduli spaces

Facilitates new approaches in the study of algebraic stacks

Abstract

We show that every quasi-compact and quasi-separated algebraic stack can be approximated by a noetherian algebraic stack. We give several applications such as eliminating noetherian hypotheses in the theory of good moduli spaces.