Lemma 28.33.11. Fibres of unramified morphisms.

Let $X$ be a scheme over a field $k$. The structure morphism $X \to \mathop{\mathrm{Spec}}(k)$ is unramified if and only if $X$ is a disjoint union of spectra of finite separable field extensions of $k$.

If $f : X \to S$ is an unramified morphism then for every $s \in S$ the fibre $X_ s$ is a disjoint union of spectra of finite separable field extensions of $\kappa (s)$.

## Comments (3)

Comment #2245 by comment on

Comment #2247 by JuanPablo on

Comment #2280 by Johan on