mathlib documentation

algebraic_geometry.morphisms.universally_closed

Universally closed morphism #

A morphism of schemes f : X ⟶ Y is universally closed if X ×[Y] Y' ⟶ Y' is a closed map for all base change Y' ⟶ Y.

We show that being universally closed is local at the target, and is stable under compositions and base changes.

@[class]

A morphism of schemes f : X ⟶ Y is universally closed if the base change X ×[Y] Y' ⟶ Y' along any morphism Y' ⟶ Y is (topologically) a closed map.

Instances of this typeclass