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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