Lemma 31.27.3. Let $X$ be a locally Noetherian integral scheme. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Let $s, s' \in \mathcal{K}_ X(\mathcal{L})$ be nonzero meromorphic sections of $\mathcal{L}$. Then $f = s/s'$ is an element of $R(X)^*$ and we have

as Weil divisors.

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