Definition:Morphism of Schemes of Finite Type

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 of finite type if and only if $f$ is locally of finite type and quasi-compact.

Sources

• 1977: Robin Hartshorne: Algebraic Geometry $\S \text{II}.3$