Theorems · Definition · algebraic geometry
AlgebraicGeometry.geometrically
CategoryTheory.ObjectProperty AlgebraicGeometry.Scheme → CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme
A morphism of schemes f : X ⟶ Y is geometrically P if for any field K and
morphism Spec K ⟶ Y, the base change X ×[Y] Spec K satisfies P.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- Fieldproof · cited by 7,404
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- CategoryTheory.ObjectPropertystatement and proof · cited by 798
- AlgebraicGeometry.Specproof · cited by 626
- CategoryTheory.IsPullbackproof · cited by 320
Cited by34
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.pullback_of_geometricallystatement and proof · cited by 3
- AlgebraicGeometry.geometrically_iff_of_isClosedUnderIsomorphismsstatement and proof · cited by 3
- AlgebraicGeometry.GeometricallyIntegral.eq_geometricallystatement · cited by 2
- AlgebraicGeometry.GeometricallyIrreducible.eq_geometricallystatement · cited by 2
- AlgebraicGeometry.geometrically_eq_universallystatement and proof · cited by 2
- AlgebraicGeometry.GeometricallyConnected.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyConnected.eq_geometricallystatement · cited by 1
- AlgebraicGeometry.GeometricallyIntegral.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyIrreducible.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyReduced.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.GeometricallyReduced.eq_geometricallystatement · cited by 1