Lemma 52.27.5. Let $(A, \mathfrak m)$ be a regular local ring. Then the Picard group of the punctured spectrum of $A$ is trivial.

Proof. Combine Divisors, Lemma 31.28.3 with More on Algebra, Lemma 15.121.2. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).