Note on local structure of Artin stacks

TL;DR

This paper demonstrates that Artin stacks with finite inertia are locally isomorphic to quotients of affine schemes by general linear group actions, providing insight into their local structure.

Contribution

It establishes a local isomorphism characterization of Artin stacks with finite inertia, linking them to quotient stacks of affine schemes by linear groups.

Findings

Artin stacks with finite inertia are etale locally quotient stacks.

Provides a local description of such stacks in terms of affine schemes and linear group actions.

Enhances understanding of the local structure of Artin stacks.

Abstract

In this note we show that an Artin stack with finite inertia stack is etale locally isomorphic to the quotient of an affine scheme by an action of a general linear group.