On the local quotient structure of Artin stacks

By Jarod Alper. 2009

52 citations recorded by the source corpus.

Abstract We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds etale locally and we provide some evidence for this conjecture. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space, generalizing the results of Pinkham and Rim. We provide a generalization and stack-theoretic proof of Luna’s etale slice theorem which shows that GIT quotient stacks are etale locally quotients stacks by the stabilizer.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c190bdfbcc786268f5cf308ee38c48e2f909701a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Jack Hall
2. David Rydh
3. Jarod Alper
4. Philipp Gross

In Mathematical Physics

1. Jack Hall
2. David Rydh
3. Jarod Alper
4. Yaron Lipman
5. Nimrod Segol

Citations in the corpus

• Coherent Tannaka duality and algebraicity of Hom-stacks (2014, methodology): “en X has quasi-affine or quasi-finite diagonal. Main applications. In work with J. Alper [AHR15], Theorem 1.1 is applied to resolve Alper’s conjecture on the local quotient structure of algebraic stacks [Alp10]. A more immediate application of Theorem 1.1 is the following algebraicity result for Hom-st”