residue_descResidueField — Mathlib

English

The germ map composed with the residue map equals the evaluation map.

Русский

Герма, затем резидуум, равна карте оценки.

LaTeX

$$$$ \mathrm{germ}_{U}(x) \circ \mathrm{residue}_x = \mathrm{evaluation}_{U}(x). $$$$

Lean4

@[reassoc (attr := simp)]
theorem residue_descResidueField {K : Type u} [Field K] {X : Scheme.{u}} {x} (f : X.presheaf.stalk x ⟶ .of K)
    [IsLocalHom f.hom] : X.residue x ≫ X.descResidueField f = f :=
  CommRingCat.hom_ext <| RingHom.ext fun _ ↦ rfl

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