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:
“Such is oftenest the young man’s introduction to the forest, and the most original part of himself. He goes thither at first as a hunter and fisher, until at last, if he has the seeds of a better life in him, he distinguishes his proper objects, as a poet or naturalist it may be, and leaves the gun and fish-pole behind. The mass of men are still and always young in this respect.”
—Henry David Thoreau (1817–1862)