Timeline for Artin approximation theorems over non-regular rings/non-Noetherian rings
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2013 at 14:10 | vote | accept | Dmitry Kerner | ||
| Feb 28, 2013 at 20:37 | answer | added | Laurent Moret-Bailly | timeline score: 6 | |
| Feb 28, 2013 at 12:02 | comment | added | user29720 | @Dmitry: My memory was a bit faulty, sorry. Looking back at that paper (which is indeed the one I had in mind), the 2nd paragraph of section 2 indicates that one can establish the analogues of what Artin proved in his earlier paper(s), but not something stronger. | |
| Feb 28, 2013 at 8:46 | history | edited | Dmitry Kerner |
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| Feb 28, 2013 at 8:37 | comment | added | Dmitry Kerner | Probably I miss smth, but in the paper "A rigid analytic version of M. Artin's theorem on analytic equations" he seems to consider polynomial equations. At least this is the statement on page 1. | |
| Feb 27, 2013 at 22:36 | comment | added | user29720 | For (1), it still seems reasonable only to consider finitely many analytic equations (since the local ring is noetherian, after all), and at least in the non-archimedean case I believe there is a paper of Siegfried Bosch on this generalization of Artin's result (i.e., considering analytic equations over $R$, not just polynomial equations over $R$). I don't remember the exact title, but if you search for papers of Bosch with "Artin" or "approximation" in the title then you should find it. | |
| Feb 27, 2013 at 20:29 | history | asked | Dmitry Kerner | CC BY-SA 3.0 |