Lemma 37.16.6. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of schemes over $S$. Assume

1. $X$ is locally of finite presentation over $S$,

2. $X$ is flat over $S$, and

3. $Y$ is locally of finite type over $S$.

Then the set

$U = \{ x \in X \mid X\text{ flat at }x \text{ over }Y\} .$

is open in $X$ and its formation commutes with arbitrary base change.

Proof. This is a special case of Lemma 37.16.5. $\square$

There are also:

• 2 comment(s) on Section 37.16: Critère de platitude par fibres

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).