Lemma 98.12.4. Let $S$ be a locally Noetherian scheme. Let $f : U \to V$ be a morphism of schemes locally of finite type over $S$. Let $u_0 \in U$ be a finite type point. The following are equivalent
$f$ is smooth at $u_0$,
$f$ viewed as an object of $(\mathit{Sch}/V)_{fppf}$ over $U$ is versal at $u_0$.
Comments (0)