Theorems · Theorem · algebraic geometry

AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv_assoc

∀ {X : AlgebraicGeometry.Scheme} {K : Type u} [inst : Field K] [inst_1 : IsAlgClosed K]
  (f : X ⟶ AlgebraicGeometry.Spec (CommRingCat.of K)) [inst_2 : AlgebraicGeometry.LocallyOfFiniteType f] (x : ↥X)
  (hx : IsClosed {x}) {Z : AlgebraicGeometry.Scheme} (h : AlgebraicGeometry.Spec (CommRingCat.of K) ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.residueFieldIsoBase f x hx).inv) h =
    CategoryTheory.CategoryStruct.comp (X.fromSpecResidueField x) (CategoryTheory.CategoryStruct.comp f h)

Defined in

Mathlib.AlgebraicGeometry.AlgClosed.Basic

Cited by

0 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsAlgClosedAlgebraicGeometry.LocallyOfFiniteType