Luna's fundamental lemma for diagonalizable groups

Dan Abramovich, Michael Temkin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study relatively affine actions of a diagonalizable group G on locally noetherian schemes. In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a G-equivariant morphism f: X' → X to be strongly equivariant, namely the base change of the morphism f∥G of quotient schemes, and establish descent criteria for f∥G to be an open embedding, étale, smooth, regular, syntomic, or lci.

Original languageAmerican English
Pages (from-to)77-113
Number of pages37
JournalAlgebraic Geometry
Issue number1
StatePublished - 1 Jan 2018

Bibliographical note

Publisher Copyright:
© Foundation Compositio Mathematica 2018.


  • Diagonalizable groups
  • Luna's fundamental lemma


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