Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsLocallyNoetherian.component_noetherian
∀ {X : AlgebraicGeometry.Scheme} [self : AlgebraicGeometry.IsLocallyNoetherian X] (U : ↑X.affineOpens),
IsNoetherianRing ↑(X.presheaf.obj (Opposite.op ↑U))- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- Set.Elemstatement · cited by 7,166
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCoverproof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zeroproof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_of_iSup_eq_topproof · cited by 1
- AlgebraicGeometry.isLocallyNoetherian_Specproof · cited by 0
- AlgebraicGeometry.isLocallyNoetherian_of_isOpenImmersionproof · cited by 0