Skip to main content
MathOverflow

You are not logged in. Your edit will be placed in a queue until it is peer reviewed.

We welcome edits that make the post easier to understand and more valuable for readers. Because community members review edits, please try to make the post substantially better than how you found it, for example, by fixing grammar or adding additional resources and hyperlinks.

10
  • 1
    $\begingroup$ See the Historical Notes of Bourbaki's Commutative Algebra. I believe they say the general notion of localization (not just domains) was isolated by Uzkov in 1940 or so. $\endgroup$
    – KConrad
    Commented Apr 19, 2010 at 22:46
  • $\begingroup$ General category construction is due to Gabriel and Gabriel-Zisman $\endgroup$
    – Shizhuo Zhang
    Commented Apr 19, 2010 at 22:48
  • $\begingroup$ Why is this community wiki? Surely there ought to be an answer to this question. $\endgroup$
    – José Figueroa-O'Farrill
    Commented Apr 19, 2010 at 23:22
  • 1
    $\begingroup$ Well, there's the obvious stupid answer: on an affine scheme, restriction to distinguished open sets corresponds to localization of the ring. It seems rather clear that localization is a good name for this, especially since you can look at smaller and smaller open sets around a point. Everything else (e.g. stalks being localization) can be understood as the same idea taken to extremes (limits). $\endgroup$
    – Ilya Grigoriev
    Commented Apr 20, 2010 at 1:48
  • 1
    $\begingroup$ Dear Harry, As an aside: the role of localization as a technical tool in commutative algebra is due to Bourbaki, I think. If you look in Zariski--Samuel, say, it does not play the same role. One certainly shouldn't be looking back before the 20th century (when very little abstract algebra existed), but rather in the middle (loosely speaking) of the 20th century. (Based on the dates in my answer below, and the date provided by Keith Conrad, I would say that the answer lies in the literature between the 1930s and the 1960s.) $\endgroup$
    – Emerton
    Commented Apr 20, 2010 at 17:19