Timeline for Pro-representability of deformation functor associated to a DG Lie algebra
Current License: CC BY-SA 3.0
10 events
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| Mar 23, 2017 at 10:06 | comment | added | Louis-Clément LEFÈVRE | Yes, I'm working more and more with coalgebras. And also I try to use the filtration of unital coalgebras which is dual to the sequence of quotients of a complete local algebras by the powers of the maximal ideal. In case these are finite-dimensional, this seems to give a proof. | |
| Mar 16, 2017 at 1:18 | comment | added | Daniel Robert-Nicoud | Never mind, I would basically have recovered Hinich's result you put in your edit (using more general results). I really think you need some kind of finite-dimensionality assumption if you want to dualize. I would advise working with coalgebras. It can be a bit hard to get used to it, but once you're familiar with the objects then everything becomes very natural. | |
| Mar 14, 2017 at 16:12 | comment | added | Louis-Clément LEFÈVRE | I'm sorry I'm not familiar with operads. But anyway I need to understand this theorems and what could go wrong. What result do you obtain ? | |
| Mar 14, 2017 at 11:03 | history | edited | Louis-Clément LEFÈVRE | CC BY-SA 3.0 |
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| Mar 7, 2017 at 22:08 | answer | added | Yonatan Harpaz | timeline score: 3 | |
| Mar 7, 2017 at 15:18 | comment | added | Daniel Robert-Nicoud | I think I have something close to what you would like, but not exactly that. I can write it as an answer in the next couple of days if you want. I just need to know: how familiar are you with the language of operads? | |
| Mar 7, 2017 at 13:34 | comment | added | Louis-Clément LEFÈVRE | Exactly I want to work in the non-DG case ("classical deformation theory" à la Schlessinger) and it seems that to get this theorem, one has to go through higher deformation theories (DG Artin rings, coalgebras, simplicial sets...) That's why I'm having such a hard time coming back to the classical case ! | |
| Mar 7, 2017 at 13:23 | comment | added | Daniel Robert-Nicoud | Do you work with dg Artin rings or just Artin rings concentrated in degree $0$? I'm think all the results you stated fail in the dg case, but there is a good chance that everything works out more or less as you want in the non-dg case. | |
| Mar 6, 2017 at 14:41 | review | First posts | |||
| Mar 6, 2017 at 14:51 | |||||
| Mar 6, 2017 at 14:39 | history | asked | Louis-Clément LEFÈVRE | CC BY-SA 3.0 |