Definition 50.15.3. Let $X \to S$ be a morphism of schemes. Let $Y \subset X$ be an effective Cartier divisor. Assume the de Rham complex of log poles is defined for $Y \subset X$ over $S$. Then the complex

$\Omega ^\bullet _{X/S}(\log Y)$

constructed in Lemma 50.15.2 is the de Rham complex of log poles for $Y \subset X$ over $S$.

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