Timeline for Intersection of Hilbert class fields of imaginary quadratic fields
Current License: CC BY-SA 3.0
10 events
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Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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Sep 21, 2012 at 0:23 | comment | added | Dror Speiser | Leaving the solution to the other question aside, torsion points of a CM elliptic curve generate the abelian extensions of the hilbert class field of the relevant quadratic field. So, this question is one level before the CM version of the linked question: here you want an intersection before taking torsion points, but just the defining field of the elliptic curve. So it's not exactly the CM version, but it's related. It's just a comment, and I'm not sure how to pursue it. (Also, I did not realise before that you asked the other question as well.) | |
Sep 20, 2012 at 21:58 | comment | added | Adam Harris | @Dror: I think in the question you link to, as JSE comments, it is really a group theoretic question about $SL_2(\mathbb{Z}_p)\times SL_2(\mathbb{Z}_p)$. For an elliptic curve with CM by $\mathcal{O}$, a CM version of the other question would be talking about the extra structure on the Tate module as a rank 1 $\mathcal{O} \otimes \mathbb{Z}_p$-module. I see this question having more to do with the action of $Pic(\mathcal{O})$ on the Hilbert class field. I'm struggling to see the whole picture at the moment with CM curves, could you please expand a little as to the similarities you see? | |
Sep 20, 2012 at 18:56 | comment | added | Dror Speiser | This is similar to a CM version of this question: mathoverflow.net/questions/74906/… | |
Sep 20, 2012 at 18:34 | vote | accept | Adam Harris | ||
Sep 20, 2012 at 12:20 | answer | added | stankewicz | timeline score: 8 | |
Sep 20, 2012 at 11:17 | answer | added | Filippo Alberto Edoardo | timeline score: 2 | |
Sep 20, 2012 at 10:55 | history | edited | Filippo Alberto Edoardo |
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Sep 20, 2012 at 10:50 | history | edited | Adam Harris |
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Sep 20, 2012 at 9:17 | history | asked | Adam Harris | CC BY-SA 3.0 |