Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsLocallyArtinian.of_isLocallyNoetherian_of_discreteTopology
∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsLocallyNoetherian X] [DiscreteTopology ↥X],
AlgebraicGeometry.IsLocallyArtinian X- Defined in
- Mathlib.AlgebraicGeometry.Artinian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- DiscreteTopologystatement and proof · cited by 373
- AlgebraicGeometry.IsLocallyNoetherianstatement and proof · cited by 31
- AlgebraicGeometry.IsLocallyArtinianstatement · cited by 12
- topologicalKrullDim_zero_of_discreteTopologyproof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.