Timeline for Split rank of inner forms
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 9, 2018 at 8:54 | comment | added | Keerthi Madapusi | @LSpice As I mentioned, the only non-trivial input is Steinberg's theorem on the existence of rational representatives of conjugacy classes in simply connected, quasi-split groups. This is Theorem 1.7 of his paper 'Regular elements of semisimple algebraic groups' and holds for any perfect field. So Langlands' proof definitely applies to all char 0 non-arch local fields. I'm not sure what happens in char p. | |
| Jul 6, 2018 at 21:16 | comment | added | LSpice | @KeerthiMadapusiPera, it's a little hard to tell ($F$ starts off being global, but then explicit reference is made to $F = \mathbb R$ and $F = \mathbb C$), but does that reference handle non-Archimedean local fields? | |
| Jan 31, 2018 at 1:52 | comment | added | Cheng-Chiang Tsai | Thanks a lot, Keerthi! I have a vague memory about Tasho mentioning a result like this due to Langlands. Good that I can trust my memory a bit more ... :) | |
| Jan 28, 2018 at 4:38 | comment | added | Keerthi Madapusi | The result is actually due to Langlands. See Lemma 2.1 of his 'On the classification of representations of real algebraic groups'. It's also probably worth noting that the main content is a theorem of Steinberg on the existence of rational points in rational conjugacy classes of simply connected semisimple groups. | |
| Jan 26, 2018 at 11:44 | history | edited | LSpice | CC BY-SA 3.0 |
Removed spurious justification for isomorphism
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| Jan 26, 2018 at 4:13 | comment | added | Cheng-Chiang Tsai | Thank you, Loren! Both the beautiful fact and this application is wonderful to learn from you. | |
| Jan 26, 2018 at 4:13 | vote | accept | Cheng-Chiang Tsai | ||
| Jan 26, 2018 at 3:43 | comment | added | YCor | The ref: Raghunathan, M. S. Tori in quasi-split-groups. J. Ramanujan Math. Soc. 19 (2004), no. 4, 281-287. | |
| Jan 26, 2018 at 3:30 | history | edited | LSpice | CC BY-SA 3.0 |
Deleted 'obvious' remark
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| Jan 26, 2018 at 3:29 | comment | added | LSpice | This is a beautiful fact that I've been waiting to use ever since Stephen pointed it out to me this summer. It is due to Raghunathan; see mathscinet.ams.org/mathscinet-getitem?mr=2125504 . | |
| Jan 26, 2018 at 3:20 | comment | added | Cheng-Chiang Tsai | Loren, I believe you have exactly pointed out what I don't know! How do we have that every torus in $G$ transfers to $G^*$? | |
| Jan 26, 2018 at 3:10 | history | answered | LSpice | CC BY-SA 3.0 |