Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isReduced_of_isReduced_stalk
∀ (X : AlgebraicGeometry.Scheme) [∀ (x : ↥X), IsReduced ↑(X.presheaf.stalk x)], AlgebraicGeometry.IsReduced X
- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsReduced
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- 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
- map_zeroproof · cited by 1,614
- AlgebraicGeometry.Scheme.Opensproof · cited by 1,149
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsReduced.of_openCoverproof · cited by 2