Timeline for Are there noncommutative extensions of $\alpha_p$ by $\mathbb{G}_m$?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2014 at 0:06 | vote | accept | Question Mark | ||
| Oct 10, 2014 at 23:12 | answer | added | Jacob Lurie | timeline score: 18 | |
| Oct 10, 2014 at 22:31 | comment | added | Fernando Muro | In case this helps, by standard group cohomology, the non-abelian central extensions of two abelian groups $A$ and $B$ are classified by $\hom(\wedge^2A,B)$, where $\wedge^2A$ is the quotient of $A\otimes A$ by the diagonal elements $a\otimes a$, $a\in A$. All this is about discrete groups, not algebraic groups. | |
| Oct 10, 2014 at 20:55 | comment | added | Question Mark | I am a little worried that Oort may be considering only commutative extensions to begin with. At any rate, leafing through his book I couldn't find it, so a precise reference would be very helpful. | |
| Oct 10, 2014 at 20:40 | comment | added | Question Mark | The latter (I thought this was standard notation), so it is a finite group scheme. In other words, $\alpha_p$ is the Frobenius kernel of $\mathbb{G}_a$. Could you give a more precise reference within LNM 15? | |
| Oct 10, 2014 at 20:13 | comment | added | anon | What is $\alpha_p$? The additive group $\mathbb{G}_a$ or the finite group scheme with $\alpha_p(R)=\{a\in R|a^p=0\}$. If the latter, there are no nontrivial extensions, see Oort 1966, LNM 15. | |
| Oct 10, 2014 at 19:36 | comment | added | Question Mark | OK, I've clarified this. | |
| Oct 10, 2014 at 19:32 | history | edited | Question Mark | CC BY-SA 3.0 |
added 150 characters in body
|
| Oct 10, 2014 at 19:04 | comment | added | R.P. | Actually, I know of no serious source that uses that phrase to mean an extension of the form $0 \rightarrow A \rightarrow E \rightarrow B \rightarrow 0$, but I would love to be shown an example. | |
| Oct 10, 2014 at 18:23 | comment | added | Matthias Wendt | Could you please specify in the question which way the extension goes? The terminology "extension of A by B" is somewhat ambiguous. | |
| Oct 10, 2014 at 17:56 | history | asked | Question Mark | CC BY-SA 3.0 |