Definition 65.28.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.

We say $f$ is

*locally of finite presentation*if the equivalent conditions of Lemma 65.22.1 hold with $\mathcal{P} =$“locally of finite presentation”.Let $x \in |X|$. We say $f$ is of

*finite presentation at $x$*if there exists an open neighbourhood $X' \subset X$ of $x$ such that $f|_{X'} : X' \to Y$ is locally of finite presentation^{1}.A morphism of algebraic spaces $f : X \to Y$ is

*of finite presentation*if it is locally of finite presentation, quasi-compact and quasi-separated.

## Comments (2)

Comment #4863 by Heejong Lee on

Comment #5149 by Johan on