Timeline for The number of types of maximal orders in a definite quaternion algebra containing a certain order
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 3 at 0:35 | comment | added | Kimball | Pick a basis of $\mathcal O(s)$. For each basis element $\alpha$, you can enumerate the elements of $\mathcal O$ with the same charpoly. So look at the possible images of the basis and see which give ring monomorphisms. Practically, you should first check to see if this is already implemented in Magma. | |
| Feb 2 at 5:40 | comment | added | Andy | @Kimball Could you elaborate on that? | |
| Feb 2 at 0:08 | comment | added | Kimball | Yes, but it shouldn't be too hard to check if there's an embedding. | |
| Feb 1 at 16:28 | comment | added | Andy | @Kimball I'm interested in proving if $t_s$ is fixed or in size $\mathcal{O}(\log p)$ when $B$ is a quaternion algebra ramified at $p$ and $\infty$ (if that is the case) in general. By computing the maximal orders, do you mean computing a representation for each isomorphism class of maximal orders? I suppose even if the representation does not contain $\mathcal{O}(s)$, there might be a conjugate of it containing $\mathcal{O}(s)$. | |
| Feb 1 at 13:49 | comment | added | Kimball | Can't you just compute the maximal orders, and see which ones contain $\mathcal O(s)$? | |
| Jan 31 at 14:01 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Jan 31 at 14:00 | history | edited | Andy | CC BY-SA 4.0 |
added 9 characters in body
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| S Jan 31 at 13:20 | review | First questions | |||
| Jan 31 at 14:32 | |||||
| S Jan 31 at 13:20 | history | asked | Andy | CC BY-SA 4.0 |