Lemma 70.8.1. Let $S$ be a scheme and let $X$ be a locally Noetherian algebraic space over $S$. Let $D \subset X$ be an effective Cartier divisor. If $X$ is $(S_ k)$, then $D$ is $(S_{k - 1})$.

Proof. By our definition of the property $(S_ k)$ for algebraic spaces (Properties of Spaces, Section 65.7) and Lemma 70.6.2 this follows from the case of schemes (Divisors, Lemma 31.15.5). $\square$

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