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The Stacks project

Lemma 71.7.3. Let S be a scheme. Let X be an algebraic space over S. Let D_1, D_2 be effective Cartier divisors on X. Let D = D_1 + D_2. Then there is a unique isomorphism

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

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

Proof. Omitted. \square


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