The Stacks project

Exercise 111.66.6. Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $x \in X(k)$ be a closed point on $X$. Let $U = X \setminus \{ x\} $. What can you say about the kernel of the restriction map $\mathop{\mathrm{Pic}}\nolimits (X) \to \mathop{\mathrm{Pic}}\nolimits (U)$?

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View Exercise 111.66.6 as pdf