Timeline for Units in quaternionic algebras
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 30, 2022 at 10:59 | comment | added | William of Baskerville | And one more question. Can one find an explicit formula for a non-zero group homomorphism $H\to\mathbb Z$? | |
| May 30, 2022 at 8:49 | comment | added | William of Baskerville | This is a very nice topic. I was wondering about the statement on the abelianization of $H\subseteq SL(2,\mathbb R)$ being $\mathbb Z^{2g}$. If $H$ acts freely on the hyperbolic plane then I can see an argument involving universal cover. Do you know an explicit reference for the general case? | |
| Apr 23, 2011 at 19:08 | comment | added | akula | @David Loeffler: Could you expand a bit on your "favourite case"? Does this description give the rank of the abelianization of the unit group in this case? | |
| Apr 19, 2011 at 23:45 | vote | accept | akula | ||
| Apr 14, 2011 at 7:45 | history | edited | David Loeffler | CC BY-SA 3.0 |
corrected an error pointed out by David Speyer; added 3 characters in body
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| Apr 14, 2011 at 7:45 | comment | added | David Loeffler | @akula: I've added some remarks on S-units. @David Speyer: Yes, I am sure you are right. | |
| Apr 14, 2011 at 7:39 | history | edited | David Loeffler | CC BY-SA 3.0 |
typo
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| Apr 13, 2011 at 17:29 | comment | added | David E Speyer | Should it be twice the genus? I'm not sure, but that seems right to me, since the abelianization of $\pi_1$ of a genus $g$ curve has rank $2g$. | |
| Apr 13, 2011 at 14:28 | comment | added | akula | @David Loeffler: Thanks. The finiteness of the unit group in the definite case must be easy -- following just by looking at the norm form. Your explanation of the the indefinite easy really explains what is going on. Do you have anything to add about S-units? | |
| Apr 13, 2011 at 7:34 | history | edited | David Loeffler | CC BY-SA 3.0 |
corrected typo
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| Apr 13, 2011 at 7:27 | history | answered | David Loeffler | CC BY-SA 3.0 |