Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.FormallyUnramified
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is formally unramified if for each affine U ⊆ Y and
V ⊆ f ⁻¹' U, The induced map Γ(Y, U) ⟶ Γ(X, V) is formally unramified.
See FormallyUnramified.hom_ext and FormallyUnramified.of_hom_ext
for the infinitesimal lifting criterion.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.formallyUnramified_appLEstatement · cited by 2
- AlgebraicGeometry.Etale.iff_flat_and_formallyUnramifiedstatement and proof · cited by 1
- AlgebraicGeometry.FormallyUnramified.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.FormallyUnramified.formallyUnramified_appLEstatement and proof · cited by 1
- AlgebraicGeometry.formallyUnramified_iffstatement and proof · cited by 1
- AlgebraicGeometry.Etale.of_compstatement and proof · cited by 0
- AlgebraicGeometry.Etale.of_formallyUnramified_of_flatstatement and proof · cited by 0
- AlgebraicGeometry.FormallyUnramified.formallyUnramified_of_affine_subsetstatement · cited by 0
- AlgebraicGeometry.FormallyUnramified.hom_extstatement and proof · cited by 0
- AlgebraicGeometry.FormallyUnramified.of_compstatement and proof · cited by 0
- AlgebraicGeometry.FormallyUnramified.of_hom_extstatement · cited by 0
- AlgebraicGeometry.FormallyUnramified.recOnstatement and proof · cited by 0