Theorem 41.16.1. Let $f : X \to S$ be a morphism that is locally of finite presentation. The following are equivalent

$f$ is étale,

for all affine $S$-schemes $Y$, and closed subschemes $Y_0 \subset Y$ defined by square-zero ideals, the natural map

\[ \mathop{\mathrm{Mor}}\nolimits _ S(Y, X) \longrightarrow \mathop{\mathrm{Mor}}\nolimits _ S(Y_0, X) \]is bijective.

## Comments (0)