Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.asFiberHom
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) → (x : ↥X) → AlgebraicGeometry.Spec (X.residueField x) ⟶ AlgebraicGeometry.Scheme.Hom.fiber f (f x)The κ(x)-point of f ⁻¹' {f x} corresponding to x.
- Defined in
- Mathlib.AlgebraicGeometry.Fiber
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberιstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.asFiberHom_applystatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueFieldstatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.range_asFiberHomstatement · cited by 0
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberι_assocstatement and proof · cited by 0