A Luna etale slice theorem for algebraic stacks

Jarod Alper, Jack Hall, David Rydh

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We prove that every algebraic stack, locally of finite type over an algebraically closed field with affine stabilizers, is etale-locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group. The proof uses an equivariant version of Artin's algebraization theorem proved in the appendix. We provide numerous applications of the main theorems.

Original languageEnglish (US)
Pages (from-to)675-738
Number of pages64
JournalAnnals of Mathematics
Issue number3
StatePublished - May 2020


  • Algebraic stacks
  • Equivariant geometry
  • Moduli spaces
  • Quotients

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'A Luna etale slice theorem for algebraic stacks'. Together they form a unique fingerprint.

Cite this