Timeline for Decomposition of linear groups into free products
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2018 at 17:57 | comment | added | Ian Agol | For higher dimensional varieties, one ought to be able to take valuations associated to ideal points and get actions on Bruhat-Tits buildings, and hence presentations as a complex of groups (generalizing the notion of a graph of groups). However, I don't know a reference immediately. | |
| Aug 20, 2018 at 16:32 | comment | added | user127776 | @ulrich Thanks that was helpful but still Soule works over polynomial rings with one variable. I'm not sure but one might able to generalized his work for curves but I imagine things doesn't work well for higher dimensional varieties. In my opinion local fields seems to be an essential part of the Bruhat-Tits building which you have access to them only when you work with curves over finite fields. I suspect one might need Parshin's Bruhat-Tits buildings for higher dimensional local fields for general varieties, which looks like they are not well studied. | |
| S Aug 20, 2018 at 13:16 | history | suggested | Uriya First | CC BY-SA 4.0 |
Fixed a misprint in the statement of Serre's generalization of Nagao's result: "variety" should be "curve".
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| Aug 20, 2018 at 9:36 | comment | added | naf | For GL_n, or more generally a Chevalley group, there is a generalisation of Nagao's theorem by C.Soule, "Chevalley groups over polynomial rings". | |
| Aug 20, 2018 at 9:19 | comment | added | Uri Bader | Note that $\text{SL}_3(\mathbb{Z})$ and $\text{SL}_3(\mathbb{F}_p[t])$ have Serre's property FA: every action on a tree has a fixed point. | |
| Aug 20, 2018 at 7:55 | review | Suggested edits | |||
| S Aug 20, 2018 at 13:16 | |||||
| Aug 20, 2018 at 5:25 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added link to the paper
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| Aug 20, 2018 at 4:29 | history | edited | user127776 | CC BY-SA 4.0 |
edited body
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| Aug 20, 2018 at 1:48 | history | asked | user127776 | CC BY-SA 4.0 |