Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIntegral_appTop_of_universallyClosed
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.UniversallyClosed f] [AlgebraicGeometry.IsAffine Y],
(CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop f)).IsIntegralIf f : X ⟶ Y is universally closed and Y is affine,
then the map on global sections is integral.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isField_of_universallyClosedproof · cited by 1