Timeline for units in distinct division algebras over number fields---are they definitely not isomorphic as abstract groups?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2010 at 3:07 | history | edited | Ben Wieland | CC BY-SA 2.5 |
serious error
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| Jun 18, 2010 at 0:15 | comment | added | Ben Wieland | Oops...no compact factors is a problem. Super-rigidity doesn't tell us anything about compact factors. The compact factors are the ones with ramification, the ones we really want to know about, so I retract most of it. But I still claim that if $H(\mathbb Q)\cong G(\mathbb Q)$, then for all $S$, $H(\mathbb Z[S^{-1}])$ and $G(\mathbb Z[S^{-1}])$ contain finite index subgroups which are identified by the given map. I don't know if that buys us anything. Rank is at least 2 because we're split at $\mathbb R$, but in general, we could take $S$ large. | |
| Jun 17, 2010 at 20:26 | comment | added | Victor Protsak | I've had a hard time following: can you, please, state your claim precisely? Also, all rigidity theorems have some hypotheses (rank at least 2, Zariski dense, no relatively compact factors), how do you deal with that for anisotropic groups? | |
| Jun 17, 2010 at 20:03 | history | answered | Ben Wieland | CC BY-SA 2.5 |