Theorems · Theorem · algebraic geometry

AlgebraicGeometry.SpecMap_residueFieldIsoBase_inv

∀ {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}),
  AlgebraicGeometry.Spec.map (AlgebraicGeometry.residueFieldIsoBase f x hx).inv =
    CategoryTheory.CategoryStruct.comp (X.fromSpecResidueField x) f

Defined in

Mathlib.AlgebraicGeometry.AlgClosed.Basic

Cited by

2 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsAlgClosedAlgebraicGeometry.LocallyOfFiniteType