Lemma 50.4.1. Let $p : X \to S$ be a morphism of schemes. The cup product on $H^*_{dR}(X/S)$ is associative and graded commutative.

**Proof.**
This follows from Cohomology, Lemmas 20.31.5 and 20.31.6 and the fact that $\wedge $ is associative and graded commutative.
$\square$

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