Timeline for a question on CM elliptic curves
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 5, 2013 at 20:31 | comment | added | Damian Rössler | I think this follows from the fact that the (exponential) Faltings height of a CM elliptic curve is (up to algebraic factors) given by its period (computed in this case by the Chowla-Selberg formula). Note that the period and the Faltings height are basically the same because the Hodge structure splits in the CM case - this is not so for a general elliptic curve. | |
| Jul 4, 2013 at 22:30 | comment | added | ACL | One aspect of the question - assumed by the formulation but nontrivial otherwise - is that all CM elliptic curves are automatically defined over the field of algebraic numbers and correspond to lattices commensurable with the ring of integers of an imaginary quadratic field. (By the Schneider-Lang theorem, this mutual algebraicity property is characteristic of CM ell. curves; if an element $\tau$ of the upper half-plane is algebraic, non-quadratic, then $j(\tau)$ is transcendental.) | |
| Jul 4, 2013 at 20:08 | comment | added | André Henriques | Dear @user36475, you might want to edit the title of your question and make it more descriptive. In that way, in the future, people who search through the list of all questions will know what it's about. | |
| Jul 4, 2013 at 18:18 | answer | added | user61789 | timeline score: 2 | |
| Jul 4, 2013 at 7:58 | comment | added | Joe Silverman | I don't have the book handy, but this looks like some of the results in Lang's Elliptic Functions book, part of which is on CM. | |
| Jul 4, 2013 at 7:35 | comment | added | Yemon Choi | Where did you come across this question, and why do you know the result is true? | |
| Jul 4, 2013 at 7:25 | review | First posts | |||
| Jul 4, 2013 at 9:21 | |||||
| Jul 4, 2013 at 7:06 | history | asked | user36475 | CC BY-SA 3.0 |