The Stacks project

Definition 50.15.1. Let $X \to S$ be a morphism of schemes. Let $Y \subset X$ be an effective Cartier divisor. We say the de Rham complex of log poles is defined for $Y \subset X$ over $S$ if for all $y \in Y$ and local equation $f \in \mathcal{O}_{X, y}$ of $Y$ we have

  1. $\mathcal{O}_{X, y} \to \Omega _{X/S, y}$, $g \mapsto g \text{d}f$ is a split injection, and

  2. $\Omega ^ p_{X/S, y}$ is $f$-torsion free for all $p$.

Comments (3)

Comment #9052 by ZL on

Typo: " is -torsion free for all " should be " is -torsion free for all ".

Comment #9179 by on

No! The sentence already says "for all in " and we really want this to be true for all . Maybe I misunderstood your comment?

Comment #9314 by ZL on

Thanks for the clarification. I was being silly!

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