Timeline for Is there $t\in\operatorname{Gal}(\overline{K}/K)$ s.t. $\operatorname{rank}_{\mathbf{Z}_p}((t-1)E_{p^\infty}(\overline{K}))=1$?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 27, 2015 at 16:48 | vote | accept | The Thin Whistler | ||
| Dec 27, 2015 at 13:47 | comment | added | Jeff Yelton | Actually, there is an easier way to see that the Galois image can't contain a (nontrivial) power of a transvection $A \in \mathrm{SL}(T_{p}(E))$ for any CM elliptic curve. Suppose $A$ were in the image; then $A$ is also in the image of $\mathrm{End}(E)$ (provided we enlarge the base field appropriately), and $A - I$ would be in the image of $\mathrm{End}(E)$. But $A - I$ is nilpotent, contradicting the fact that $\mathrm{End}(E)$ is a domain. | |
| Dec 27, 2015 at 11:01 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
improved formatting
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| Dec 26, 2015 at 18:42 | history | edited | Jeff Yelton | CC BY-SA 3.0 |
edited body
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| Dec 26, 2015 at 18:32 | history | answered | Jeff Yelton | CC BY-SA 3.0 |