Definition 115.23.9. Let $X$ be a scheme. Let $\{ D_ i\} _{i \in I}$ be a locally finite collection of effective Cartier divisors on $X$. Suppose given a function $I \to \mathbf{Z}_{\geq 0}$, $i \mapsto n_ i$. The *sum of the effective Cartier divisors* $D = \sum n_ i D_ i$, is the unique effective Cartier divisor $D \subset X$ such that on any quasi-compact open $U \subset X$ we have $D|_ U = \sum _{D_ i \cap U \not= \emptyset } n_ iD_ i|_ U$ is the sum as in Divisors, Definition 31.13.6.

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