Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.PartialMap.comp_restrict_right

∀ {X Y Z : AlgebraicGeometry.Scheme} [inst : PreirreducibleSpace ↥X] [inst_1 : Nonempty ↥Y] (f : X.PartialMap Y)
  [inst_2 : AlgebraicGeometry.IsDominant f.hom] (g : Y.PartialMap Z) (V : Y.Opens) (hV : Dense ↑V) (hV' : V ≤ g.domain),
  f.comp (g.restrict V hV hV') =
    (f.comp g).restrict
      ((AlgebraicGeometry.Scheme.Hom.opensFunctor f.domain.ι).obj ((TopologicalSpace.Opens.map f.hom.base).obj V)) ⋯ ⋯

Defined in

Mathlib.AlgebraicGeometry.Birational.Composition

Cited by

1 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PreirreducibleSpaceNonemptyAlgebraicGeometry.IsDominant