Lemma 33.16.8. Let $f : X \to Y$ be a morphism of schemes locally of finite type over a base scheme $S$. Let $x \in X$ be a point. Set $y = f(x)$ and assume that $\kappa (y) = \kappa (x)$. Then the following are equivalent

$\text{d}f : T_{X/S, x} \longrightarrow T_{Y/S, y}$ is injective, and

$f$ is unramified at $x$.

## Comments (2)

Comment #2159 by Ariyan on

Comment #2191 by Johan on