The Stacks project

Remark 50.15.9. Let $S$ be a locally Noetherian scheme. Let $X$ be locally of finite type over $S$. Let $Y \subset X$ be an effective Cartier divisor. If for every $y \in Y$ we can find a diagram of schemes over $S$

\[ X \xleftarrow {\varphi } U \xrightarrow {\psi } V \]

with $\varphi $ étale and $\psi |_{\varphi ^{-1}(Y)} : \varphi ^{-1}(Y) \to V$ étale, then the de Rham complex of log poles is defined for $Y \subset X$ over $S$. A special case is when the pair $(X, Y)$ étale locally looks like $(V \times \mathbf{A}^1, V \times \{ 0\} )$. If we ever need this result we will formulate a precise statement and add a proof here.

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