Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eq

∀ {X Y U : AlgebraicGeometry.Scheme} (f : U ⟶ X) (g : X ⟶ Y) [inst : AlgebraicGeometry.IsOpenImmersion f]
  [inst_1 : AlgebraicGeometry.LocallyOfFinitePresentation g],
  (TopologicalSpace.Opens.map f.base).obj (AlgebraicGeometry.Scheme.Hom.smoothLocus g) =
    AlgebraicGeometry.Scheme.Hom.smoothLocus (CategoryTheory.CategoryStruct.comp f g)

Defined in

Mathlib.AlgebraicGeometry.Morphisms.Smooth

Cited by

1 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.IsOpenImmersionAlgebraicGeometry.LocallyOfFinitePresentation