Timeline for working with local rings: "abstract" vs "geometric" proofs
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 7, 2014 at 7:59 | vote | accept | Dmitry Kerner | ||
| Aug 7, 2014 at 7:59 | history | edited | Dmitry Kerner | CC BY-SA 3.0 |
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| Jul 15, 2014 at 22:09 | answer | added | MathChump | timeline score: 1 | |
| Feb 18, 2013 at 6:36 | comment | added | Dmitry Kerner | @Mahdi: the initial Artin's theorem addresses the ring of complex analytic functions! i.e. precisely the good case: you can compute each such function at points close to the origin. see my upd. | |
| Feb 17, 2013 at 21:18 | comment | added | Mahdi Majidi-Zolbanin | There is Artin's Approximation Theorem, which I think is similar to the question you are asking. But then I see that you already asked a question about Artin's Approximation Theorem before, so that tells me this is not what you are looking for? | |
| Feb 17, 2013 at 19:31 | history | edited | Dmitry Kerner | CC BY-SA 3.0 |
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| Feb 17, 2013 at 19:15 | comment | added | Dmitry Kerner | @Mahdi: precisely. That's what I'm asking. For which statements about the local rings it is enough to check the statement just for e.g. localization/henselization of an affine ring? | |
| Feb 17, 2013 at 17:58 | comment | added | Mahdi Majidi-Zolbanin | @Dmitry: Many properties hold for a local ring if and only if they hold for its completion. | |
| Feb 17, 2013 at 17:29 | comment | added | Dmitry Kerner | @Eric Wofsey: I speak about a statement formulated over an arbitrary local ring. Maybe complete, maybe not. Can't see how Cohen's structure theorem can be helpful here. | |
| Feb 17, 2013 at 16:52 | comment | added | Eric Wofsey | This may not be exactly what you're looking for, but if the statement you're trying to prove can be reduced to the completion of your local ring, you can use the Cohen structure theorem (en.wikipedia.org/wiki/Cohen_structure_theorem). | |
| Feb 17, 2013 at 16:20 | history | asked | Dmitry Kerner | CC BY-SA 3.0 |