Timeline for How to prove that $A$ is supersingular iff the Picard number $\rho(A)$ is equal to the second $l$-adic Betti number $b_2(A) = 6$?
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| Jun 16, 2016 at 18:05 | comment | added | Dimitri Koshelev | Thank you. Am I right that all proof is carried to finite fields case unless supersingular elliptic curves over $\mathbb{F}_q$ need not be isogenous over $\mathbb{F}_q$? Hence $\rho(A/\mathbb{F}_q) = 6$ iff $A$ is $\mathbb{F}_q$-supersingular, but $A$ can be $\mathbb{F}_q$-isogenous a direct product of two $\mathbb{F}_q$-non-isogenous supersingular elliptic curves over $\mathbb{F}_q$ with $\rho(A/\mathbb{F}_q) = 2$. | |
| Jun 15, 2016 at 7:39 | history | answered | Yuri Zarhin | CC BY-SA 3.0 |