Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReduced
∀ (X : AlgebraicGeometry.Scheme), AlgebraicGeometry.IsIntegral X ↔ IrreducibleSpace ↥X ∧ AlgebraicGeometry.IsReduced X
- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCat.carrierstatement and proof · cited by 3,184
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.IsIntegralstatement and proof · cited by 45
- IrreducibleSpacestatement and proof · cited by 40
- AlgebraicGeometry.IsReducedstatement and proof · cited by 38
- AlgebraicGeometry.isIntegral_of_irreducibleSpace_of_isReducedproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyIntegral.isIntegral_of_subsingletonproof · cited by 0