Theorems · Definition · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.residue
(X : AlgebraicGeometry.LocallyRingedSpace) → (x : ↑X.toTopCat) → X.presheaf.stalk x ⟶ X.residueField x
The residue map from the stalk to the residue field.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.PresheafedSpace.presheafstatement and proof · cited by 1,104
- CommRingCat.carrierproof · cited by 1,096
- TopCat.Presheaf.stalkstatement and proof · cited by 407
- CommRingCat.ofHomproof · cited by 259
- AlgebraicGeometry.LocallyRingedSpacestatement and proof · cited by 205
- AlgebraicGeometry.LocallyRingedSpace.toTopCatstatement and proof · cited by 128
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyRingedSpace.evaluationproof · cited by 6
- AlgebraicGeometry.LocallyRingedSpace.evaluation_naturalityproof · cited by 4
- AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residuestatement and proof · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.residue_comp_residueFieldMap_eq_stalkMap_comp_residue_assocstatement and proof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.residue_surjectivestatement · cited by 0