Lemma 50.23.4. Let $X \to S$ and $i : Z \to X$ be as in Lemma 50.23.3. The gysin map $\gamma ^ p$ is compatible with the de Rham differentials on $\Omega ^\bullet _{X/S}$ and $\Omega ^\bullet _{Z/S}$.

**Proof.**
We may check this locally and then it follows from Lemma 50.23.2.
$\square$

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