Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zero
∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsLocallyNoetherian X],
topologicalKrullDim ↥X ≤ 0 → AlgebraicGeometry.IsLocallyArtinian X- Defined in
- Mathlib.AlgebraicGeometry.Artinian
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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.Iso.homproof · cited by 7,684
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- TopCat.carrierstatement and proof · cited by 3,184
- LE.le.transproof · cited by 3,151
- 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
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isLocallyArtinianScheme_Specproof · cited by 0