Theorems · Theorem · algebraic geometry
AlgebraicGeometry.GeometricallyReduced.isReduced_of_flat_of_isLocallyNoetherian
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.GeometricallyReduced f] [AlgebraicGeometry.Flat f]
[AlgebraicGeometry.IsReduced Y] [AlgebraicGeometry.IsLocallyNoetherian Y], AlgebraicGeometry.IsReduced X- Cited by
- 2 results in Mathlib
- Foundations
- Depth 238 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CategoryTheory.Precoverage.ZeroHypercover.pullback₁proof · cited by 64
- AlgebraicGeometry.Scheme.affineCoverproof · cited by 61
- AlgebraicGeometry.Flatstatement and proof · cited by 49
- AlgebraicGeometry.IsReducedstatement and proof · cited by 38
- AlgebraicGeometry.IsLocallyNoetherianstatement and proof · cited by 31
- AlgebraicGeometry.GeometricallyReducedstatement and proof · cited by 8
- AlgebraicGeometry.IsReduced.of_openCoverproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyIntegral.isIntegral_of_subsingletonproof · cited by 0