Timeline for $G(k)/H(k)$ as a submanifold of $G/H(k)$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 2, 2019 at 23:47 | answer | added | thierry stulemeijer | timeline score: 5 | |
| Nov 11, 2018 at 15:39 | vote | accept | D_S | ||
| Nov 11, 2018 at 7:18 | answer | added | Venkataramana | timeline score: 7 | |
| Nov 11, 2018 at 1:57 | comment | added | YCor | OK: these are precisely the nondiscrete locally compact fields. | |
| Nov 10, 2018 at 23:48 | comment | added | D_S | I just mean $\mathbb R, \mathbb C$, or a finite extension of $\mathbb Q_p$ or $\mathbf F_q((t))$ | |
| Nov 10, 2018 at 22:33 | comment | added | YCor | Borel-Serre (CMH 1964) obtains the finiteness of the relevant cohomology groups when one has a perfect field with finitely many extensions of each degree. This probably yields the openness result in this case. The openness result fails for the non-perfect locally compact field $K=\mathbf{F}_p((t))$ and $G\to G/H$ for $G=\mathrm{SL}_p$, $H=\mathrm{PGL}_p$. | |
| Nov 10, 2018 at 22:29 | comment | added | YCor | Would you specify what you call a local field? Everybody agrees that $\mathbf{Q}_p$ is a local field, but some define it as an arbitrary nondiscrete locally compact field (which is a reasonable setting for your question), while others would exclude $\mathbf{R}$ but would allow some non-locally compact fields such as Laurent Series over infinite discrete fields. | |
| Nov 10, 2018 at 21:24 | history | asked | D_S | CC BY-SA 4.0 |