Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.GeometricallyIntegral
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropWe say that morphism f : X ⟶ Y is geometrically integral if for all Spec K ⟶ Y with K
a field, X ×[Y] Spec K is integral.
- Cited by
- 9 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 by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyIntegral.eq_geometricallystatement · cited by 2
- AlgebraicGeometry.GeometricallyIntegral.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.geometricallyIntegral_iffstatement and proof · cited by 1
- AlgebraicGeometry.isCommMonObj_of_isProper_of_geometricallyIntegralstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.iff_geometricallyIntegral_fiberstatement · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.geometrically_isIntegralstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.isIntegral_of_isLocallyNoetherianstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.isIntegral_of_subsingletonstatement and proof · cited by 0
- AlgebraicGeometry.GeometricallyIntegral.recOnstatement and proof · cited by 0