Timeline for conjugacy classes in anisotropic semisimple groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 14, 2014 at 3:05 | comment | added | Venkataramana | Jim Humphreys' comments contain an answer and references to your new question | |
| Jan 13, 2014 at 8:25 | comment | added | Rupert | Okay, great, thanks, what happens in positive characteristic? Is it still true then that elements of $G(k)$ are always semisimple? | |
| Jan 11, 2014 at 5:25 | history | edited | Venkataramana | CC BY-SA 3.0 |
added 637 characters in body
|
| Jan 10, 2014 at 15:33 | history | edited | Venkataramana | CC BY-SA 3.0 |
char k=0 is necessary for the semi-simplicity of the elements of $G(k)$.
|
| Jan 10, 2014 at 15:28 | comment | added | Venkataramana | It is easy to give a proof (in char 0). If $g\in G(k)$ then write $g=g_sg_u$ (Jordan decomposition). If $g_u\neq 1$, then every unipotent element is char zero lies in the unipotent radical of a parabolic subgroup $P$ defined over $k$, and hence the group $G$ is isotropic over $k$ (you can also use Jacobson-Morozov, to get a split torus). | |
| Jan 10, 2014 at 15:25 | history | edited | Venkataramana | CC BY-SA 3.0 |
edited body
|
| Jan 10, 2014 at 14:53 | comment | added | Rupert | I find it quite interesting that you say that the elements of $G(k)$ are always semisimple; are you able to give me a reference for that? | |
| Jan 10, 2014 at 14:52 | vote | accept | Rupert | ||
| Jan 10, 2014 at 14:31 | comment | added | Jim Humphreys | It's probably helpful to give a reference for the first sentence. At least in characteristic 0, this is made explicit in Cor. 9.4 of Groupes reductifs (IHES Publ. Math. 1965) by Borel-Tits, available online at numdam.org. (Note too the spelling "Zariski".) | |
| Jan 10, 2014 at 12:09 | history | answered | Venkataramana | CC BY-SA 3.0 |