Exercise 111.43.6. Let $X$ be a scheme (or a locally ringed space). The rule $U \mapsto \mathcal{O}_ X(U)^*$ defines a sheaf of groups denoted $\mathcal{O}_ X^*$. Briefly explain why the Picard group of $X$ (Definition 111.40.7) is equal to $H^1(X, \mathcal{O}_ X^*)$.

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