Timeline for Does this condition reduce to the correct notion of irreducibility on schemes?
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
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| Oct 18, 2010 at 4:13 | vote | accept | Harry Gindi | ||
| Oct 18, 2010 at 4:13 | |||||
| Mar 22, 2010 at 13:36 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 38 characters in body
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| Mar 22, 2010 at 13:30 | history | edited | Harry Gindi | CC BY-SA 2.5 |
added 169 characters in body; added 148 characters in body; added 74 characters in body
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| Mar 22, 2010 at 12:38 | comment | added | JBorger | OK, this is ridiculous. Apologies for all the confusion. An etale map of sheaves is defined to be one that's formally etale and locally of finite presentaiton. | |
| Mar 22, 2010 at 10:53 | history | edited | Harry Gindi | CC BY-SA 2.5 |
Clarified per Jim Borger's comments
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| Mar 22, 2010 at 10:17 | comment | added | Harry Gindi | Isn't that just a smooth morphism then? | |
| Mar 22, 2010 at 10:00 | answer | added | Daniel Bergh | timeline score: 2 | |
| Mar 21, 2010 at 23:55 | comment | added | JBorger | Oops! An etale monomorphism, of course! (Also, in (2) I meant that such a map of sheaves is defined to be etale if it is formally smooth and locally of finite presentation.) | |
| Mar 21, 2010 at 23:53 | comment | added | Georges Elencwajg | James, surely you don't mean what you wrote in (1): an étale morphism isn't an open immersion in general. | |
| Mar 21, 2010 at 22:41 | comment | added | JBorger | The following clarifications might help some people (and are presumably what fpqc meant): (1) a morphism of schemes is an open immersion if and only if it is etale, (2) a morphism of sheaves is etale if and only if it is formally etale and locally of finite presentation (by which one means satisfying the usual functorial characterizations of these concepts for schemes), (3) a morphism of sheaves is defined (by fpqc) to be an open immersion if and only if it is an etale monomorphism. I guess the key question is whether an open immersion, so defined, is representable. | |
| Mar 21, 2010 at 20:56 | comment | added | Shizhuo Zhang | Unknown: fpqc has explained what Spec(0) means. | |
| Mar 21, 2010 at 20:51 | comment | added | Qfwfq | Never heard about Spec(0). | |
| Mar 21, 2010 at 20:49 | comment | added | Shizhuo Zhang | No, I don't think we have such notions because the reason you mentioned. | |
| Mar 21, 2010 at 19:36 | comment | added | Andrea Ferretti | Ok, I have decided to remove all the comments, but please, try to leave things more consequential. | |
| Mar 21, 2010 at 19:16 | comment | added | Harry Gindi | I hope it's less confusing now. | |
| Mar 21, 2010 at 19:16 | history | edited | Harry Gindi | CC BY-SA 2.5 |
edited body
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| Mar 21, 2010 at 19:10 | comment | added | Andrea Ferretti | I have a problem with notation: what do you mean by Spec(0)? The spectrum of the 0 ring, that is, the empty scheme? And second, what do you mean when you say that fiber product of schemes does not agree with fiber product of the underlying topological spaces in the case of open immersions? Can you give a counterexample? | |
| Mar 21, 2010 at 18:53 | history | asked | Harry Gindi | CC BY-SA 2.5 |