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Nov 15, 2018 at 9:11 comment added Tyler Lawson @TimCampion Sorry that I didn't see this. Yes, but I think the fact that "completion is an instance of Bousfield localization" is something that's a little surprising when first encountered and really requires something derived.
Oct 17, 2018 at 19:19 comment added Tim Campion Interesting, thanks! Unless I'm mistaken, the class of abelian groups which are local with respect to all maps $A \to B$ such that $A_{(p)} \to B_{(p)}$ is an isomorphism is precisely the $\mathbb Z_{(p)}$-modules, which makes this example look closer to the derived analog. But I believe the class of abelian groups which are local with respect to all maps $A \to B$ such that $A/p \to B/p$ is an isomorphism is just the $\mathbb Z/p$-modules, which looks further from the derived analog.
Oct 17, 2018 at 9:16 history answered Tyler Lawson CC BY-SA 4.0