Proper Morphism

In algebraic geometry, a proper morphism between schemes is a scheme-theoretic analogue of a proper map between complex-analytic varieties.

A basic example is a complete variety (e.g., projective variety) in the following sense: a k-variety X is complete in the classical definition if it is universally closed. A proper morphism is a generalization of this to schemes.

A closed immersion is proper. A morphism is finite if and only if it is proper and quasi-finite.