Timeline for Central extensions of group schemes
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2011 at 23:25 | vote | accept | Michael Thaddeus | ||
| Aug 23, 2011 at 6:06 | comment | added | Minhyong Kim | Heh. I see my kneejerk response was very naive. I will leave the comment up anyways, so others can learn from my silliness. | |
| Aug 23, 2011 at 5:50 | answer | added | Torsten Ekedahl | timeline score: 14 | |
| Aug 23, 2011 at 3:44 | comment | added | Michael Thaddeus | I concur with Scott. What if $S=\mu_n\times_k\mu_n$, for example? (Of course when the characteristic does not divide n, the group scheme is étale and we return immediately to the category of groups...) | |
| Aug 23, 2011 at 3:40 | comment | added | David Ben-Zvi | In the additive case there are interesting central extensions of $G_a$ over a finite field, the "fake Heisenberg groups" whose representation theory is a motivating example in the works of Boyarchenko and Drinfeld. | |
| Aug 23, 2011 at 3:10 | comment | added | Minhyong Kim | Scott: You're probably right. The argument is OK when the characteristic of $k$ doesn't divide $n$, but I suppose all the fun is when it does. I'll think about it some more. | |
| Aug 23, 2011 at 2:51 | comment | added | S. Carnahan♦ | @Minhyong: It seems that $\mu_n(S)$ is not cyclic for general $S$. I don't quite follow your argument, so I don't know if this is a problem. | |
| Aug 23, 2011 at 1:12 | comment | added | Minhyong Kim | Unless I'm missing some subtlety, this should be true by using the functor of points. That is, you will get an exact sequence $1\rightarrow A(S) \rightarrow B(S) \rightarrow C(S)$ for every $k$-scheme $S$. Now, any subgroup of a cyclic group is cyclic, so what you want should follow from the usual fact. | |
| Aug 22, 2011 at 23:06 | history | asked | Michael Thaddeus | CC BY-SA 3.0 |