Timeline for Compact elements in $G(K)$ for a reductive group $G$ over a nonarchimedean local field $K$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2014 at 12:34 | comment | added | Venkataramana | @user52484: Yes, thank you for pointing this out; otherwise you may have a product of anisotropic and isotropic simply connected groups, for which KT cannot hold. | |
| Oct 14, 2014 at 2:31 | comment | added | user27920 | @Venkataramana: Of course, one really intends to impose the additional (harmless in practice) assumption that if $G$ is "absolutely simple" (or at least $K$-simple) for Kneser-Tits, to avoid the silliness of $K$-anisotropic direct factors. | |
| Oct 13, 2014 at 23:29 | comment | added | Venkataramana | This is called the "Kneser-Tits conjecture" for local fields and has been proved by various people; there is a proof (by Raghunathan and Prasad) by reducing this to groups of $K$-rank one. Note also that Kneser-Tits is false for many fields; it is a relatively recent result due to Gille (I think) that KT is true for number fields. | |
| Oct 13, 2014 at 21:35 | comment | added | Question Mark | Why is a semi-simple, simply connected, isotropic $G$ generated by unipotent elements? | |
| Oct 13, 2014 at 3:54 | history | answered | Venkataramana | CC BY-SA 3.0 |