Lemma 31.14.4. Let $S$ be a scheme. Let $D_1$, $D_2$ be effective Cartier divisors on $S$. Let $D = D_1 + D_2$. Then there is a unique isomorphism

$\mathcal{O}_ S(D_1) \otimes _{\mathcal{O}_ S} \mathcal{O}_ S(D_2) \longrightarrow \mathcal{O}_ S(D)$

which maps $1_{D_1} \otimes 1_{D_2}$ to $1_ D$.

Proof. Omitted. $\square$

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