The Stacks project

Lemma 29.30.11. Let $f : X \to S$ be a morphism of schemes. If $f$ is flat, locally of finite presentation, and all fibres $X_ s$ are local complete intersections, then $f$ is syntomic.

Proof. Clear from Lemmas 29.30.9 and 29.30.10 and the isomorphisms of local rings $ \mathcal{O}_{X, x}/\mathfrak m_ s \mathcal{O}_{X, x} \cong \mathcal{O}_{X_ s, x} $. $\square$

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