Definition
A morphism f : X → Y of algebraic varieties or more generally of schemes, is called universally closed if for all morphisms Z → Y, the projections for the fiber product
are closed maps of the underlying topological spaces. A morphism f : X → Y of algebraic varieties is called proper if it is separated and universally closed. A morphism of schemes is called proper if it is separated, of finite type and universally closed ( II, 5.4.1 ). One also says that X is proper over Y. A variety X over a field k is complete when the structural morphism from X to the spectrum of k is proper.
Read more about this topic: Proper Morphism
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