Theorems · Theorem · algebraic geometry

AlgebraicGeometry.finite_appTop_of_universallyClosed

∀ {X : AlgebraicGeometry.Scheme} (K : Type u) [inst : Field K] (f : X ⟶ AlgebraicGeometry.Spec (CommRingCat.of K))
  [AlgebraicGeometry.IsIntegral X] [AlgebraicGeometry.UniversallyClosed f] [AlgebraicGeometry.LocallyOfFiniteType f],
  (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appTop f)).Finite

If X is an integral scheme that is universally closed and of finite type over Spec K, then Γ(X, ⊤) is a finite field extension over K.

Defined in

Mathlib.AlgebraicGeometry.Morphisms.Proper

Cited by

0 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAlgebraicGeometry.IsIntegralAlgebraicGeometry.UniversallyClosedAlgebraicGeometry.LocallyOfFiniteType