@[implicit_reducible]

noncomputable instance AlgebraicGeometry.Scheme.openSubschemeOverSpec (k : Type u) [Field k] (X : Scheme) [X.Over (Spec (CommRingCat.of k))] (U : X.Opens) : (↑U).Over (Spec (CommRingCat.of k))

The structure map making an open subscheme of X into a scheme over Spec k, obtained by composing the open immersion with the structure map of X.

theorem AlgebraicGeometry.Scheme.isAlgebraicVariety_openSubscheme (k : Type u) [Field k] (X : Scheme) [X.Over (Spec (CommRingCat.of k))] [hX : IsAlgebraicVariety k X] (U : X.Opens) : IsAlgebraicVariety k ↑U

Lecture 2, Corollary 4: an open subspace U of an algebraic variety X over k is itself an algebraic variety over k.