Lemma 64.4.7. Let $S$ be a scheme. Let $f : X \to T$ be a morphism of algebraic spaces over $S$. Let $s : T \to X$ be a section of $f$ (in a formula $f \circ s = \text{id}_ T$). Then

$s$ is representable, locally of finite type, locally quasi-finite, separated and a monomorphism,

if $f$ is locally separated, then $s$ is an immersion,

if $f$ is separated, then $s$ is a closed immersion, and

if $f$ is quasi-separated, then $s$ is quasi-compact.

## Comments (2)

Comment #451 by Kestutis Cesnavicius on

Comment #453 by Johan on