Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsLocallyArtinian
AlgebraicGeometry.Scheme → Prop
A scheme X is locally Artinian if 𝒪ₓ(U) is Artinian for all affine U.
- Defined in
- Mathlib.AlgebraicGeometry.Artinian
- Cited by
- 12 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 by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isLocallyArtinian_iff_openCoverstatement and proof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.iff_isLocallyNoetherian_and_discreteTopologystatement and proof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zerostatement · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_locallyQuasiFinitestatement and proof · cited by 2
- AlgebraicGeometry.IsArtinianScheme.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.IsLocallyArtinian.of_isImmersionstatement and proof · cited by 1
- AlgebraicGeometry.IsLocallyArtinian.of_isLocallyNoetherian_of_discreteTopologystatement · cited by 1
- AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCoverstatement and proof · cited by 0
- AlgebraicGeometry.IsArtinianScheme.recOnstatement and proof · cited by 0
- AlgebraicGeometry.IsFinite.of_locallyQuasiFinitestatement and proof · cited by 0
- AlgebraicGeometry.IsLocallyArtinian.casesOnstatement and proof · cited by 0