Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.LocallyOfFinitePresentation
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is locally of finite presentation if for each affine U ⊆ Y
and V ⊆ f ⁻¹' U, The induced map Γ(Y, U) ⟶ Γ(X, V) is of finite presentation.
- Cited by
- 26 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 by30
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.smoothLocusstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.fppfPrecoverageproof · cited by 4
- AlgebraicGeometry.Scheme.fppfPrecoverage_le_fpqcPrecoverageproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.finitePresentation_appLEstatement · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.mem_smoothLocusstatement and proof · cited by 2
- AlgebraicGeometry.locallyOfFinitePresentation_iffstatement and proof · cited by 1
- AlgebraicGeometry.LocallyOfFinitePresentation.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.LocallyOfFinitePresentation.finitePresentation_appLEstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eqstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.isLocallyConstructible_imagestatement and proof · cited by 1
- AlgebraicGeometry.Etale.iff_flat_and_formallyUnramifiedstatement and proof · cited by 1