Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsLocallyArtinian.of_isImmersion
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsImmersion f]
[AlgebraicGeometry.IsLocallyArtinian Y], AlgebraicGeometry.IsLocallyArtinian X- Defined in
- Mathlib.AlgebraicGeometry.Artinian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.IsImmersionstatement and proof · cited by 17
- AlgebraicGeometry.IsLocallyArtinianstatement and proof · cited by 12
- AlgebraicGeometry.Scheme.Hom.isEmbeddingproof · cited by 7
- Topology.IsEmbedding.discreteTopologyproof · cited by 6
- AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherianproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isLocallyArtinian_iff_of_isOpenCoverproof · cited by 0