Lemma 10.136.13. A relative global complete intersection is syntomic, i.e., flat.

**Proof.**
Let $R \to S$ be a relative global complete intersection. The fibres are global complete intersections, and $S$ is of finite presentation over $R$. Thus the only thing to prove is that $R \to S$ is flat. This is true by (2) of Lemma 10.136.12.
$\square$

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