Timeline for Algebraic, analytic, formal modules
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
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| Aug 10, 2010 at 12:55 | history | edited | Dmitry Kerner | CC BY-SA 2.5 |
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| Aug 9, 2010 at 9:22 | answer | added | Mohan | timeline score: 2 | |
| Aug 9, 2010 at 0:43 | vote | accept | Dmitry Kerner | ||
| Aug 7, 2010 at 12:00 | comment | added | BCnrd | Dear Manish: I don't think that formal GAGA can be useful here, since it requires completeness of the base ring. It's closer in spirit to issues around Artin approximation (but the latter doesn't seem to help much either, as far as I can tell). | |
| Aug 7, 2010 at 9:37 | answer | added | Mohan | timeline score: 1 | |
| Aug 7, 2010 at 3:12 | answer | added | Hailong Dao | timeline score: 4 | |
| Aug 7, 2010 at 2:18 | comment | added | Manish Kumar | I don't know of a counter example if you restrict to analytically irreducible singularities. I am not sure why you exactly need this for but as Brian said, looking at the Henselianization of the left ring might be a good idea. If you are interested in GAGA type result then there is a formal GAGA. Of course the setup is different but its in similar spirit. | |
| Aug 7, 2010 at 1:14 | history | edited | Dmitry Kerner | CC BY-SA 2.5 |
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| Aug 7, 2010 at 0:31 | comment | added | BCnrd | The ring on the left should be henselization (just think of Artin-Popescu approximation, noting that algebraic and analytic local rings are excellent), which would also remove Manish Kumar's example. Faithfulness is obvious from faithful flatness of completion. By "surjective" do you mean what is usually called "essentially surjective"? | |
| Aug 7, 2010 at 0:29 | history | edited | BCnrd | CC BY-SA 2.5 |
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| Aug 6, 2010 at 23:40 | comment | added | Manish Kumar | I think it fails for a node in the plane, i.e. $f=y^2-x^2-x^3$. When you pass to completion it becomes reducible. $\mathbb{C}[[x,y]]/(y-x(1+x)^{1/2})$ doesn't have a preimage. | |
| Aug 6, 2010 at 20:20 | history | edited | Dmitry Kerner | CC BY-SA 2.5 |
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| Aug 6, 2010 at 20:19 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Aug 6, 2010 at 20:18 | history | asked | Dmitry Kerner | CC BY-SA 2.5 |