Timeline for Origin of the term "localization" for the localization of a ring
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2010 at 8:32 | answer | added | Victor Protsak | timeline score: 8 | |
| Apr 20, 2010 at 18:06 | vote | accept | Harry Gindi | ||
| Apr 20, 2010 at 17:19 | comment | added | Emerton | 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.) | |
| Apr 20, 2010 at 17:00 | comment | added | Ben Webster♦ | @Jose- I'm would go so far as to say that this is policy, but I think it's a common opinion that history questions should be community wiki. I certainly wouldn't discourage people from doing so, if they choose to. | |
| Apr 20, 2010 at 16:53 | answer | added | Emerton | timeline score: 14 | |
| Apr 20, 2010 at 9:04 | answer | added | Martin Brandenburg | timeline score: 5 | |
| Apr 20, 2010 at 2:00 | comment | added | Ilya Grigoriev | Sorry for not reading your question carefully. I don't think the term is older than the concept of affine schemes, before that people probably just called it "adding inverses" or something. However, I don't know exactly. | |
| Apr 20, 2010 at 1:55 | comment | added | Harry Gindi | Yes, this is what I mentioned in the post at the beginning. One would think that the localization of a ring came before the obviously much more complicated concept of talking the stalks of the structure sheaf. | |
| Apr 20, 2010 at 1:48 | comment | added | Ilya Grigoriev | 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). | |
| Apr 20, 2010 at 0:56 | comment | added | Harry Gindi | Anyway, I looked it up in Bourbaki, but it doesn't really give a lot of information. | |
| Apr 19, 2010 at 23:35 | comment | added | Harry Gindi | I dunno, because it's a soft question? | |
| Apr 19, 2010 at 23:22 | comment | added | José Figueroa-O'Farrill | Why is this community wiki? Surely there ought to be an answer to this question. | |
| Apr 19, 2010 at 22:48 | comment | added | Shizhuo Zhang | General category construction is due to Gabriel and Gabriel-Zisman | |
| Apr 19, 2010 at 22:46 | comment | added | KConrad | 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. | |
| Apr 19, 2010 at 22:41 | history | asked | Harry Gindi | CC BY-SA 2.5 |