Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.residueFieldCongr
{X : AlgebraicGeometry.Scheme} → {x y : ↥X} → x = y → (X.residueField x ≅ X.residueField y)The isomorphism between residue fields of equal points.
- Defined in
- Mathlib.AlgebraicGeometry.ResidueField
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Isostatement · cited by 3,963
- 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
- CategoryTheory.eqToIsoproof · cited by 97
- AlgebraicGeometry.Scheme.residueFieldstatement · cited by 95
Cited by23
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Pullback.Triplet.tensorproof · cited by 25
- AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInlproof · cited by 9
- AlgebraicGeometry.Scheme.Pullback.Triplet.tensorInrproof · cited by 9
- AlgebraicGeometry.Scheme.Hom.residueFieldMap_congrstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr'statement · cited by 2
- AlgebraicGeometry.Scheme.residueFieldCongr_fromSpecResidueFieldstatement · cited by 2
- AlgebraicGeometry.Scheme.residueFieldCongr_trans_homstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Pullback.ofPointTensor_SpecTensorToproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.residueFieldMap_congr'_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Pullback.residueFieldCongr_inv_residueFieldMap_ofPointstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.SpecToEquivOfField_eq_iffstatement and proof · cited by 1