Lemma 29.34.11. Let $f : X \to S$ be a morphism of schemes. Let $x \in X$ be a point. Let $V \subset S$ be an affine open neighbourhood of $f(x)$. The following are equivalent

The morphism $f$ is smooth at $x$.

There exists an affine open $U \subset X$, with $x \in U$ and $f(U) \subset V$ such that the induced morphism $f|_ U : U \to V$ is standard smooth.

## Comments (1)

Comment #835 by Johan Commelin on

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