Definition 81.13.1. In Situation 81.2.1 let $X/B$ be good. Assume $X$ is integral with $\dim _\delta (X) = n$. Let $f \in R(X)^*$. The principal divisor associated to $f$ is the $(n - 1)$-cycle

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

defined in Spaces over Fields, Definition 71.6.7. This makes sense because prime divisors have $\delta$-dimension $n - 1$ by Lemma 81.12.1.

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