Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsLocallyArtinian.of_locallyQuasiFinite
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyQuasiFinite f]
[AlgebraicGeometry.IsLocallyArtinian Y], AlgebraicGeometry.IsLocallyArtinian X- Cited by
- 2 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Algebraproof · cited by 11,388
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatproof · cited by 2,333
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- CommRingCat.carrierproof · cited by 1,096
- Module.Finiteproof · cited by 1,032
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- CategoryTheory.Limits.pullback.sndproof · cited by 637
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.IsFinite.of_locallyQuasiFiniteproof · cited by 0