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Oct 22, 2019 at 22:31 comment added Y_q I think you are right, I'm using Pic=Cl. Actually I encountered this when doing Hartshorne exercise 7.9, and indeed he assumed smoothness, but I don't know to what extent this condition can be weakened so that excision in Picard groups can be used, so that's why I said ''under some good conditions''.
Oct 22, 2019 at 20:04 comment added abx You seem to be assuming that $X$ is smooth (or at least locally factorial), which is definitely unnecessary.
Oct 22, 2019 at 5:05 review Late answers
Oct 22, 2019 at 6:39
Oct 22, 2019 at 4:54 history edited Y_q CC BY-SA 4.0
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Oct 22, 2019 at 4:49 review First posts
Oct 22, 2019 at 7:28
Oct 22, 2019 at 4:48 history answered Y_q CC BY-SA 4.0