Timeline for Simplicity of (complex) orthogonal groups
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 19, 2010 at 14:33 | history | edited | Skip | CC BY-SA 2.5 |
Added text on the questioner's specific group, and reference to Chernousov's result in Platonov & Rapinchuk
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| Jun 21, 2010 at 20:55 | vote | accept | JGis | ||
| Jun 21, 2010 at 21:51 | |||||
| Jun 21, 2010 at 20:42 | comment | added | BCnrd | A nice way to interpret Skip's example is that there's an exact sequence of $k$-gps $$1 \rightarrow \mu \rightarrow \widetilde{G} \rightarrow G \rightarrow 1$$ where $\widetilde{G}$ is s.c. central cover and $\mu$ is the mult. type finite center. Passing to $k$-points gives an exact sequence of pointed sets $$1 \rightarrow \widetilde{G}(k)/\mu(k) \rightarrow G(k) \rightarrow {\rm{H}}^1(k,\mu) \rightarrow {\rm{H}}^1(k,\widetilde{G})$$ with connected map a homomorphism. In many cases, final term is 1 and the 2nd-to-last term is computed by Hilbert 90 to be big (e.g., ${\rm{H}}^1(k,\mu_2)$). | |
| Jun 21, 2010 at 20:34 | history | answered | Skip | CC BY-SA 2.5 |