Timeline for Division fields of isogenous abelian varieties over a p-adic field
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 16, 2013 at 10:20 | vote | accept | Oleg Karpin | ||
| Aug 11, 2013 at 20:08 | answer | added | abz | timeline score: 4 | |
| Aug 11, 2013 at 11:15 | history | edited | Oleg Karpin | CC BY-SA 3.0 |
edited title
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| Aug 11, 2013 at 11:08 | comment | added | abz | Yes, it's induced by f, and so compatible with Galois. | |
| Aug 11, 2013 at 11:08 | comment | added | Chandan Singh Dalawat | The isogeny $f$ will be compatible with the Galois actions if it is a $K$-isogeny. | |
| Aug 11, 2013 at 11:04 | comment | added | Oleg Karpin | Thanks for pointing this out. A priori this isomorphism is an isomorphism of abstract groups, is this isomorphism in addition compatible with Galois actions? If yes, this would imply $K(A[\ell])=K(A'(\ell))$ for all $\ell\nmid \deg(f)$? | |
| Aug 11, 2013 at 10:59 | comment | added | naf | If $f:A \to A'$ is an isogeny, then $f$ induces an isomorphism from $A[l]$ onto $A'[l]$ for any $l$ prime to the degree of $f$. | |
| Aug 11, 2013 at 10:55 | review | First posts | |||
| Aug 11, 2013 at 10:57 | |||||
| Aug 11, 2013 at 10:39 | history | asked | Oleg Karpin | CC BY-SA 3.0 |