Abstract
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 language | English |
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Pages (from-to) | 77-113 |
Number of pages | 37 |
Journal | Algebraic Geometry |
Volume | 5 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2018 |
Bibliographical note
Publisher Copyright:© Foundation Compositio Mathematica 2018.
Keywords
- Diagonalizable groups
- Luna's fundamental lemma