Timeline for Conductor CM abelian variety
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 2, 2014 at 14:09 | comment | added | abx | OK, you are right. | |
| Feb 2, 2014 at 13:41 | comment | added | Joe Silverman | @abx I guess it depends whether $E/F$ having CM by $O_K$ means that $\mbox{End}(E/F)=O_K$ or $\mbox{End}(E/FK)=O_K$. But if you prefer, then consider $E_D$ to be defined over $\mathbb{Q}(i)$, and twist by a square-free $D\in\mathbb{Z}[i]$ whose norm is odd. Then the same conclusion applies. | |
| Feb 2, 2014 at 12:49 | comment | added | abx | But note that the OP asked for complex multiplication by $O_K$, which I assume is the ring of integers of $K$. Then your example $E_D$ does not apply. | |
| Feb 2, 2014 at 12:34 | history | answered | Joe Silverman | CC BY-SA 3.0 |