Theorems · Theorem · algebraic geometry
AlgebraicGeometry.noetherianSpace_of_isAffine
∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsAffine X] [IsNoetherianRing ↑(X.presheaf.obj (Opposite.op ⊤))],
TopologicalSpace.NoetherianSpace ↥X- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.invproof · cited by 6,514
- 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 and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.noetherianSpace_of_isAffineOpenproof · cited by 0