Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.descResidueField

{K : Type u} →
  [inst : Field K] →
    {X : AlgebraicGeometry.Scheme} →
      {x : ↥X} →
        (f : X.presheaf.stalk x ⟶ CommRingCat.of K) →
          [IsLocalHom (CommRingCat.Hom.hom f)] → X.residueField x ⟶ CommRingCat.of K

If K is a field and f : 𝒪_{X, x} ⟶ K is a ring map, then this is the induced map κ(x) ⟶ K.

Defined in

Mathlib.AlgebraicGeometry.ResidueField

Cited by

10 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsLocalHom