Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.GeometricallyReduced
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropWe say that morphism f : X ⟶ Y is geometrically reduced if for all Spec K ⟶ Y with K
a field, X ×[Y] Spec K is reduced.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyReduced.isReduced_of_flat_of_isLocallyNoetherianstatement and proof · cited by 2
- AlgebraicGeometry.GeometricallyReduced.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyReduced.eq_geometricallystatement · cited by 1
- AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreduciblestatement and proof · cited by 1
- AlgebraicGeometry.geometricallyReduced_iffstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyReduced.geometrically_isReducedstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyReduced.isReduced_of_flat_of_finite_irreducibleComponentsstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyReduced.recOnstatement and proof · cited by 0
- AlgebraicGeometry.smooth_of_grpObjstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.of_geometricallyReduced_of_geometricallyIrreduciblestatement and proof · cited by 0