Timeline for Is the tangent space functor from PD formal groups to Lie algebras an equivalence?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 21, 2010 at 19:16 | answer | added | Torsten Ekedahl | timeline score: 6 | |
| Jun 21, 2010 at 18:33 | history | edited | S. Carnahan♦ | CC BY-SA 2.5 |
repaired, I hope.
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| Dec 14, 2009 at 18:59 | comment | added | David Ben-Zvi | The formal completion of the tangent space at x has a canonical formal group structure, which is related to your formal completion by deformation to the normal cone. Of course this formal group is additive by construction. Maybe though you can rephrase as asking about recovering PD neighborhoods from analogues of solving Maurer-Cartan equations for some (restricted?) dgla. | |
| Dec 14, 2009 at 18:49 | comment | added | David E Speyer | I think your third paragraph, where you made the global construction, is correct. You might be able to make this an honest question by just striking out the second paragraph. | |
| Dec 14, 2009 at 18:34 | answer | added | Ben Webster♦ | timeline score: 4 | |
| Dec 12, 2009 at 22:00 | comment | added | S. Carnahan♦ | This is rather embarrassing. You're both absolutely correct. In fact, I was wondering why the "canonical" structures in my examples weren't preserved under etale maps. I will try to turn this into an honest question later today. | |
| Dec 12, 2009 at 13:28 | comment | added | Leonid Positselski | "If X is a smooth variety, then the formal completion of X at a closed point x has a canonical formal group structure" -- this is a very strange assertion, as automorphisms of the formal completion of a point on a smooth variety do not preserve any formal group structure in general, neither do those of them that come from global automorphisms of the variety. | |
| Dec 12, 2009 at 13:25 | comment | added | Tyler Lawson | Can you elaborate on how you obtain a formal group structure on the completion X^? I only know how this arises if X is a group scheme, or how to make the pair (X^, (X x X)^) into a groupoid object. | |
| Dec 12, 2009 at 8:37 | history | asked | S. Carnahan♦ | CC BY-SA 2.5 |