nLab
morphism of finite presentation

Definition

A morphism $f:Y\to X$ is finitely presented at $x\in X$ if there is an affine open neighborhood $U\ni x$ and an affine open set $V\subset Y$, $f(V)\subset U$ such that ${𝒪}_Y(V)$ is finitely generated as ${𝒪}_X(U)$-module. A morphism $f:Y\to X$ is locally finitely presented if it is finitely presented at each $x\in X$. It is finitely presented if it is locally finitely presented, quasicompact and quasiseparated.

Morphism is essentially finitely presented if it is a localization of a finitely presented morphism.

References and related concepts

• morphism of finite type
• wikipedia: Finite, quasi-finite, finite type, and finite presentation morphisms