Lemma 37.15.2. Let S be a scheme. Let
be a cartesian diagram of schemes. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Let x' \in X' with images x = g'(x') and s' = f'(x').
If \mathcal{F} is flat over S at x, then (g')^*\mathcal{F} is flat over S' at x'.
If g is flat at s' and (g')^*\mathcal{F} is flat over S' at x', then \mathcal{F} is flat over S at x.
In particular, if g is flat, f is locally of finite presentation, and \mathcal{F} is locally of finite presentation, then formation of the open subset of Theorem 37.15.1 commutes with base change.
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Comment #7756 by James on
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