Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsLocallyNoetherian
AlgebraicGeometry.Scheme → Prop
A scheme X is locally Noetherian if 𝒪ₓ(U) is Noetherian for all affine U.
- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by37
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ordstatement and proof · cited by 12
- AlgebraicGeometry.Scheme.ordHomstatement and proof · cited by 10
- AlgebraicGeometry.IsLocallyNoetherian.component_noetherianstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.ord_eq_zero_of_coheight_neq_onestatement and proof · cited by 5
- AlgebraicGeometry.Scheme.ord_eq_unzero_ordHomstatement and proof · cited by 3
- AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherianstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.ord.congr_simpstatement and proof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.iff_isLocallyNoetherian_and_discreteTopologystatement and proof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zerostatement and proof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCoverstatement and proof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_iff_openCoverstatement and proof · cited by 2
- AlgebraicGeometry.isLocallyNoetherian_of_affine_coverstatement · cited by 2