Definition:Quasi-Separated Morphism of Schemes

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 quasi-separated if and only if the diagonal morphism $\Delta_f : X \to X \times_Y X$ is quasi-compact.

Also see

• Definition:Separated Morphism of Schemes
• Definition:Proper Morphism of Schemes
• Separated Morphism is Quasi-Separated

Sources

• 1977: Robin Hartshorne: Algebraic Geometry