Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIntegral_of_irreducibleSpace_of_isReduced
∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsReduced X] [H : IrreducibleSpace ↥X], AlgebraicGeometry.IsIntegral X
- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objproof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Monoidproof · cited by 3,887
- TopCat.carrierstatement and proof · cited by 3,184
- Set.Nonemptyproof · cited by 2,627
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- 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 by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReducedproof · cited by 2
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldproof · cited by 0