Timeline for n-th root of unity in n-th division field of abelian variety?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2015 at 9:15 | comment | added | ACL | My mistake! Sorry for the confusion and thank you for your answer and your reply to my comment. | |
| Jul 1, 2015 at 12:39 | comment | added | Yuri Zarhin | Actually, $A^4$ does not have to be principally polarized. In fact, it does not have to be isomorphic to its dual. (As an example, you may take an abelian surface $A$ over an algebraically closed field $K$ with $\End(A)=\Z$ and such that $\Hom(A,A^t)$ is generated by the polarization $\lambda: A \to A^t$ with $\ker(\lambda)$ being a product of two cyclic groups of prime order $\ell \ne char(K)$.) It is $(A \times A^t)^4$, which is always principally polarized. | |
| Jul 1, 2015 at 8:42 | comment | added | ACL | It seems that one can also combine Joe Silverman's answer with your observation that $A^4$ has a principal polarization. | |
| Jun 4, 2015 at 8:32 | vote | accept | David84 | ||
| Jun 4, 2015 at 7:35 | history | edited | Yuri Zarhin | CC BY-SA 3.0 |
added 170 characters in body
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| Jun 4, 2015 at 7:27 | history | answered | Yuri Zarhin | CC BY-SA 3.0 |