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.
Read more about Proper Morphism: Definition, Examples, Properties and Characterizations of Proper Morphisms, Proper Morphism of Formal Schemes
Famous quotes containing the word proper:
“I should like to know what is the proper function of women, if it is not to make reasons for husbands to stay at home, and still stronger reasons for bachelors to go out.”
—George Eliot [Mary Ann (or Marian)