Timeline for $\text{PGL}_n(\mathbf{Q}_p)$ and the Congruence Subgroup Property
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2018 at 6:47 | comment | added | Venkataramana | see mathoverflow.net/questions/150342/… Jim Humphrey's answer about PGL vs SL | |
| Apr 27, 2018 at 3:02 | comment | added | Venkataramana | As far as I know, the congruence subgroup property (CSP) for lattices in $SL_n({\mathbb Q}_p)$ (even for $n\geq 3$) is open. When you say "CSP for $SL_n$ is known", what is known is CSP for the split $SL_n$ over a number field. Your lattices in $SL_n$ or $PGL_n$ over $p$-adic groups are cocompact and are not covered in the known cases of CSP. As to simply connected vs adjoint, there is an old Bourbaki talk by Serre on CSP where he discusses how CSP fails for non-simply connected groups even though the congruence subgroup kernel is central. | |
| Apr 27, 2018 at 2:29 | review | First posts | |||
| Apr 27, 2018 at 2:39 | |||||
| Apr 27, 2018 at 2:27 | history | asked | user72293 | CC BY-SA 3.0 |