Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isClosedImmersion_diagonal_restrict_diagonalCoverDiagonalRange
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (𝒰 : Y.OpenCover)
(𝒱 : (i : 𝒰.I₀) → (CategoryTheory.Limits.pullback f (𝒰.f i)).OpenCover)
[∀ (i : 𝒰.I₀), AlgebraicGeometry.IsAffine (𝒰.X i)]
[∀ (i : 𝒰.I₀) (j : (𝒱 i).I₀), AlgebraicGeometry.IsAffine ((𝒱 i).X j)],
AlgebraicGeometry.IsClosedImmersion
(CategoryTheory.Limits.pullback.diagonal f ∣_ AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange f 𝒰 𝒱)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isSeparated_of_injectiveproof · cited by 0