Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.residue_descResidueField
∀ {K : Type u} [inst : Field K] {X : AlgebraicGeometry.Scheme} {x : ↥X} (f : X.presheaf.stalk x ⟶ CommRingCat.of K)
[inst_1 : IsLocalHom (CommRingCat.Hom.hom f)],
CategoryTheory.CategoryStruct.comp (X.residue x) (AlgebraicGeometry.Scheme.descResidueField f) = f- Defined in
- Mathlib.AlgebraicGeometry.ResidueField
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsLocalHom
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.presheafstatement and proof · cited by 1,104
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.descResidueField_fromSpecResidueFieldproof · cited by 1
- AlgebraicGeometry.Scheme.descResidueField_stalkClosedPointTo_compproof · cited by 1
- AlgebraicGeometry.Scheme.residue_descResidueField_assocproof · cited by 0