Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.Smooth
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is smooth if for each affine U ⊆ Y and
V ⊆ f ⁻¹' U, The induced map Γ(Y, U) ⟶ Γ(X, V) is smooth.
- Cited by
- 12 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 by15
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Smooth.iff_forall_exists_isStandardSmoothstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_topstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.smooth_appLEstatement · cited by 1
- AlgebraicGeometry.Smooth.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.Smooth.smooth_appLEstatement and proof · cited by 1
- AlgebraicGeometry.SmoothOfRelativeDimension.smoothstatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iffstatement and proof · cited by 0
- AlgebraicGeometry.Smooth.exists_isStandardSmoothstatement and proof · cited by 0
- AlgebraicGeometry.Smooth.of_smooth_fiberToSpecResidueFieldstatement and proof · cited by 0
- AlgebraicGeometry.Smooth.recOnstatement and proof · cited by 0
- AlgebraicGeometry.IsSmoothproof · cited by 0
- AlgebraicGeometry.IsSmoothOfRelativeDimension.isSmoothstatement · cited by 0