Timeline for What are the local properties of schemes preserved under global sections?
Current License: CC BY-SA 3.0
10 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 23, 2013 at 7:00 | vote | accept | Damien Robert | ||
| Aug 22, 2013 at 11:19 | comment | added | Damien Robert | Yes but as Will pointed out, connectivity is not a local property, so that's why I used locally noetherian instead. But this is a good point: if a local property fails for the global sections of a non affine scheme, is there any sort of additional global property that makes it work? | |
| Aug 22, 2013 at 2:20 | answer | added | Karl Schwede | timeline score: 7 | |
| Aug 21, 2013 at 21:07 | comment | added | Eric Wofsey | It might be better to just assume all your schemes are connected for integrality. Then you don't need any noetherian hypothesis. | |
| Aug 21, 2013 at 21:02 | comment | added | Fred Rohrer | I misunderstood the question and thus deleted my answer. | |
| Aug 21, 2013 at 20:46 | comment | added | Damien Robert | Yes you are right of course! I just wanted to add another example than reduced, that's why I gave the integrality example. One could correct this as follows: a noetherian ring whose stalks are integral is a product of domain. This is a local condition, and so if I am not mistaken a "locally integral" locally noetherian scheme has global sections a product of domains also. | |
| Aug 21, 2013 at 20:31 | comment | added | Will Sawin | Integrality is not local by your definition, I don't think. A disjoint union is an open cover, and a disjoint union of integral schemes need not be integral. | |
| Aug 21, 2013 at 19:50 | history | edited | Damien Robert | CC BY-SA 3.0 |
Fix spelling in title
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| Aug 21, 2013 at 19:43 | history | asked | Damien Robert | CC BY-SA 3.0 |