Definition:Proper Morphism of Schemes
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Definition
Let $\struct {X, \OO_X}$ and $\struct {Y, \OO_Y}$ be schemes.
Let $f : \struct {X, \OO_X} \to \struct {Y, \OO_Y}$ be a morphism of schemes.
$f$ is proper if and only if $f$ is separated, of finite type and universally closed.
Sources
- 1977: Robin Hartshorne: Algebraic Geometry $\S \text{II}.4$