Timeline for Hyperspecial parahoric group schemes/Chevalley groups
Current License: CC BY-SA 3.0
8 events
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| Mar 2, 2015 at 0:22 | comment | added | LSpice | (Oops, sorry; I misspelt your name.) On further reflection (no pun intended), since we've got a split group, I return to my original position: all (hyper)special points in the (reduced) building are $G_{\text{ad}}(K)$-conjugate; this is stated in \S2.5 of Tits's Corvallis article. | |
| Mar 2, 2015 at 0:08 | comment | added | LSpice | @MartinSchuster, I'm sorry, you are right. There are at most two orbits under $G_{\text{ad}}(K)$ (not necessarily $G(K)$ as I originally said), but I don't see any obvious reason that these two orbits should give rise to the same schemes. | |
| Feb 6, 2015 at 16:44 | comment | added | Michael Schuster | Could you explain a bit more? Not all hyperspecial parahorics are conjugate in $G(K)$, but they will be conjugate over a finite extension $L$ of $K$. Are you saying conjugation in $G(L)$ will induce a $K$-isomorphism of the group schemes? | |
| Feb 5, 2015 at 19:49 | comment | added | LSpice | (Hmm, since they don't sit in a superstructure, I guess I mean that the $G(K)$-conjugacy of the associated building points induces an isomorphism of the underlying schemes.) | |
| Feb 5, 2015 at 19:33 | comment | added | LSpice | They are not just isomorphic, but $G(K)$-conjugate! From my point of view, the reason to distinguish them is not as groups, but for the way that they fit into the Bruhat--Tits picture: they correspond to different (but $G(K)$-conjugate) points in the BT building. | |
| Feb 5, 2015 at 17:27 | history | edited | Michael Schuster |
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| Feb 5, 2015 at 17:23 | review | First posts | |||
| Feb 5, 2015 at 17:42 | |||||
| Feb 5, 2015 at 17:19 | history | asked | Michael Schuster | CC BY-SA 3.0 |