Definition 70.6.7. Let $S$ be a scheme. Let $X$ be a locally Noetherian integral algebraic space over $S$. Let $f \in R(X)^*$. The principal Weil divisor associated to $f$ is the Weil divisor

$\text{div}(f) = \text{div}_ X(f) = \sum \text{ord}_ Z(f) [Z]$

where the sum is over prime divisors and $\text{ord}_ Z(f)$ is as in Definition 70.6.4. This makes sense by Lemma 70.6.6.

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