Timeline for How to show that an ind-scheme is not a scheme?
Current License: CC BY-SA 3.0
13 events
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| Jul 12, 2011 at 14:16 | history | edited | Michal Zydor | CC BY-SA 3.0 |
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| Jul 12, 2011 at 14:00 | history | edited | Michal Zydor | CC BY-SA 3.0 |
changed "regular scheme" to "scheme"
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| Jul 12, 2011 at 13:52 | vote | accept | Michal Zydor | ||
| Jul 12, 2011 at 13:44 | history | edited | Michal Zydor | CC BY-SA 3.0 |
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| Jul 12, 2011 at 8:45 | answer | added | S. Carnahan♦ | timeline score: 3 | |
| Jul 12, 2011 at 6:19 | comment | added | Martin Brandenburg | Do you really mean $k[[\epsilon]]$? If you are writing $k$-valued points above, this does not give the correct algebraic set. Perhaps you mean $k((\epsilon)) := \text{colim}_n \text{Spec}(k[x_{-n},...,x_0,x_1,...])$? | |
| Jul 12, 2011 at 5:31 | comment | added | S. Carnahan♦ | I think the easiest example is the completion of $\mathbb{A}^1_k$ at a $k$-point. As a locally ringed space, it is a topological point whose ring of functions is $k[[t]]$ - obviously not a scheme. | |
| Jul 11, 2011 at 22:03 | comment | added | Michal Zydor | Yes, that's what I'm trying to do. Just hoping for an "elementary" proof, since this seems to be the easiest example (maybe alongside with infinite dimensional vector space). | |
| Jul 11, 2011 at 21:27 | vote | accept | Michal Zydor | ||
| Jul 11, 2011 at 22:01 | |||||
| Jul 11, 2011 at 21:03 | comment | added | Martin Brandenburg | Do you want a prove that this limit does not exist in the category of schemes? In this case you may find mathoverflow.net/questions/65506/… helpful. Often people just "argue" in this case that there does not seem to be any natural model of this limit, thus it does not exist ... perhaps motivated by some sort of "good limits" in the same spirit as GIT uses good quotients. | |
| Jul 11, 2011 at 20:13 | answer | added | Jason Starr | timeline score: 5 | |
| Jul 11, 2011 at 19:27 | history | edited | Michal Zydor | CC BY-SA 3.0 |
added 210 characters in body; edited title
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| Jul 11, 2011 at 18:24 | history | asked | Michal Zydor | CC BY-SA 3.0 |