Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Etale.of_comp

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {Z : AlgebraicGeometry.Scheme} (g : Y ⟶ Z)
  [AlgebraicGeometry.Etale (CategoryTheory.CategoryStruct.comp f g)] [AlgebraicGeometry.LocallyOfFiniteType g]
  [AlgebraicGeometry.FormallyUnramified g], AlgebraicGeometry.Etale f

If f ≫ g is étale and g unramified, then f is étale.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Etale
Cited by
0 results in Mathlib
Foundations
Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.EtaleAlgebraicGeometry.LocallyOfFiniteTypeAlgebraicGeometry.FormallyUnramified
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.LocallyOfFiniteType · cited by 59AlgebraicGeometry.Locally…AlgebraicGeometry.Etale · cited by 27AlgebraicGeometry.EtaleCategoryTheory.MorphismProperty.of_postcomp · cited by 17MorphismProperty.of_postc…AlgebraicGeometry.FormallyUnramified · cited by 11AlgebraicGeometry.Formall…Etale.of_compCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.