Timeline for Colimits of schemes
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| May 8, 2010 at 17:05 | comment | added | Anton Geraschenko | "that's impossible unless dim(X)=1." I think you mean that's impossible unless dim(X/Z)=1. It may be that something with the right universal property does exist in the category of schemes, but that Z is not the only thing that gets crushed. Why should the dimension of X/Z agree with the dimension of X? | |
| Dec 29, 2009 at 13:06 | comment | added | Tyler Lawson | Let X = Spec k[x,y] and Z = Spec k[x] (the divisor y=0). Then the quotient X/Z exists in affine schemes: it is the pullback of k[x,y] -> k[x] <- k, which is the non-Noetherian subring k[y,yx,yx^2,...]. I'm not clear whether Spec of this ring is still the quotient in the category of all schemes, but I think that more is necessary to make your argument work. | |
| Dec 29, 2009 at 5:58 | history | answered | Evgeny Shinder | CC BY-SA 2.5 |