Theorems · Theorem · algebraic geometry

AlgebraicGeometry.pointEquivClosedPoint_apply_coe

∀ {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]
  (p :
    { p //
      CategoryTheory.CategoryStruct.comp p f =
        CategoryTheory.CategoryStruct.id (AlgebraicGeometry.Spec (CommRingCat.of K)) }),
  ↑((AlgebraicGeometry.pointEquivClosedPoint f) p) = ↑p (IsLocalRing.closedPoint K)

Defined in

Mathlib.AlgebraicGeometry.AlgClosed.Basic

Cited by

0 results in Mathlib

Foundations

Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldIsAlgClosedAlgebraicGeometry.LocallyOfFiniteType