Timeline for What's the name for the analogue of divided power algebras for x^i/i?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2012 at 15:29 | vote | accept | Vipul Naik | ||
| Jun 30, 2012 at 15:29 | history | bounty ended | Vipul Naik | ||
| Jun 27, 2012 at 12:23 | comment | added | Filippo Alberto Edoardo | Vipul, I think Laurent's answer is very enlightening, but as you say that you are not very familiar with crystalline cohomology I dare commenting a bit. The ring $B_{cris}$ you might have heard of is the divided power envelope of some ''universal'' creature; what Laurent observes is that one can, analogously, apply a whole bestiary of different divided power constructions to the universal creature to find many more rings which all look natural in $p$-adic Hodge theory, like $B_{cris}$. Your ''logarithmic divided power'' then corresponds to a (useful!) ring of functions with a growth condition. | |
| Jun 26, 2012 at 16:07 | comment | added | Vipul Naik | Filippo, thanks a lot for your answer. I don't know anything about crystalline cohomology, but I think I understand the rest of your answer. For the application that I had in mind, it isn't a disadvantage if the "logarithmic divided powers" are defined in a more diverse array of situations than the usual divided powers; that might even be an advantage. But I suspect that you may be right that the situations where logarithmic divided powers exist, and the usual ones don't, are not very interesting. | |
| Jun 26, 2012 at 16:02 | history | edited | Vipul Naik | CC BY-SA 3.0 |
fixed minor spelling issues
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| Jun 25, 2012 at 10:33 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
added 1 characters in body
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| Jun 25, 2012 at 10:24 | history | answered | Filippo Alberto Edoardo | CC BY-SA 3.0 |