Timeline for Is there a connected non-affine scheme $S$ such that it is the union of rings of integers of number fields?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Sep 25, 2011 at 23:01 | vote | accept | James D. Taylor | ||
| Sep 25, 2011 at 22:15 | answer | added | Qing Liu | timeline score: 28 | |
| Sep 25, 2011 at 21:30 | comment | added | Georges Elencwajg | @Ali: the glueing is only possible if $K=K'$. And when you say "the affine line", it should be $Spec(\mathbb Z)$. However your basic insight is absolutely correct (but I hadn't seen it when I started composing my answer !) | |
| Sep 25, 2011 at 21:23 | comment | added | Joël | And for the second question, you mean "open subscheme of a normal separated, irreducible scheme? Otherwise two copies of Spec $O_k$ is a counter-example. | |
| Sep 25, 2011 at 21:03 | answer | added | Georges Elencwajg | timeline score: 3 | |
| Sep 25, 2011 at 20:07 | comment | added | Joël | You mean "separated", not "separable" I suppose. | |
| Sep 25, 2011 at 19:51 | vote | accept | James D. Taylor | ||
| Sep 25, 2011 at 20:41 | |||||
| Sep 25, 2011 at 19:03 | comment | added | James D. Taylor | I'm not sure what you mean, but I want to require that $S$ be separable. | |
| Sep 25, 2011 at 19:02 | answer | added | Will Sawin | timeline score: 3 | |
| Sep 25, 2011 at 18:49 | comment | added | user16974 | Is it possible to glue $Spec (O_K)$ and $Spec(O_{K'})$ along some open set? For example consider the affine line with a double point. | |
| Sep 25, 2011 at 18:05 | history | edited | James D. Taylor | CC BY-SA 3.0 |
added 184 characters in body; edited title; added 43 characters in body
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| Sep 25, 2011 at 18:01 | comment | added | James D. Taylor | Yes, I want it to be connected, and equal to the union of Spec's of rings of integers (this implies normal, of course). I'll edit the question. | |
| Sep 25, 2011 at 17:58 | comment | added | Donu Arapura | Are you requiring the scheme to be normal in the question? That seems to be what you wanted in the discussion leading up to it. Without some hypothesis, it is trivially false: take a disjoint union of $Spec(O_K)$ with something else. | |
| Sep 25, 2011 at 17:49 | history | edited | James D. Taylor | CC BY-SA 3.0 |
added 3 characters in body; edited body
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| Sep 25, 2011 at 17:41 | history | asked | James D. Taylor | CC BY-SA 3.0 |