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Aug 20 at 3:00 comment added Brendan Murphy My first thought for a potential counterexample is $k[[x_1, x_2, \ldots]]$ but I'm not sure how you'd go about showing it's not a filtered colimit. We'd want some kind of finitary invariant of UFDs with nice properties for noetherian ones, I guess?
May 1 at 12:34 history edited Lukas Heger CC BY-SA 4.0
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May 1 at 10:58 history asked Lukas Heger CC BY-SA 4.0