Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.residueFieldMap
{X Y : AlgebraicGeometry.LocallyRingedSpace} →
(f : X ⟶ Y) → (x : ↑X.toTopCat) → Y.residueField ((CategoryTheory.ConcreteCategory.hom f.base) x) ⟶ X.residueField xIf X ⟶ Y is a morphism of locally ringed spaces and x a point of X, we obtain
a morphism of residue fields in the other direction.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.PresheafedSpace.Hom.basestatement · cited by 1,135
- AlgebraicGeometry.LocallyRingedSpace.Hom.toHomstatement · cited by 995
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturalitystatement · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_applystatement · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturalitystatement · cited by 2
- AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_idstatement · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_applystatement · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.residueFieldMap_compstatement · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue_assocstatement and proof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturality_assocstatement and proof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assocstatement and proof · cited by 0