Definition 31.13.6. Let $S$ be a scheme. Given effective Cartier divisors $D_1$, $D_2$ on $S$ we set $D = D_1 + D_2$ equal to the closed subscheme of $S$ corresponding to the quasi-coherent sheaf of ideals $\mathcal{I}_{D_1}\mathcal{I}_{D_2} \subset \mathcal{O}_ S$. We call this the sum of the effective Cartier divisors $D_1$ and $D_2$.

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