AlgebraicGeometry.Scheme.residueField

(X : AlgebraicGeometry.Scheme) → ↥X → CommRingCat

The residue field of X at a point x is the residue field of the stalk of X at x.

Defined in: Mathlib.AlgebraicGeometry.ResidueField
Cited by: 95 results in Mathlib
Foundations: Depth 88 from the axioms, rests on 1,647 definitions · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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.presheafproof · cited by 1,104
CommRingCat.carrierproof · cited by 1,096
TopCat.Presheaf.stalkproof · cited by 407
IsLocalRing.ResidueFieldproof · cited by 156

Results whose statement or proof uses this declaration.