Timeline for Is there a generalization of the "characteristic polynomial" to other split/quasi-split algebraic groups?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 8, 2016 at 13:10 | comment | added | LSpice | Which part? The idea is that, over a strictly Henselian field $F$, every (reductive) group is, not necessarily split, but quasisplit (has a Borel); and then there is a canonical, minimal splitting field for such a group (centraliser of maximal split torus is maximal torus; all maximal tori arising in this way are rationally conjugate (because maximal split tori are), hence have the same splitting field). Applying this to the centraliser of a semisimple element allows us to associate to it a canonical, minimal splitting field. | |
| Mar 8, 2016 at 4:04 | comment | added | Will Sawin | @LSpice I don't understand that, can you expand? | |
| Mar 8, 2016 at 3:46 | comment | added | LSpice | Since @JohnBinder seems to be interested in $p$-adic groups, it may be worth mentioning (anent your first sentence only) that we do have a minimal extension $E_\gamma$ if our field $F$ is strictly Henselian; for then the centraliser of a maximal $F$-split torus $A$ in $C_G(\gamma)$ is a maximal torus, whose splitting field is independent of the choice of $A$. | |
| Apr 10, 2015 at 4:31 | vote | accept | John Binder | ||
| Apr 10, 2015 at 1:32 | history | answered | Will Sawin | CC BY-SA 3.0 |