𝑝^{𝑘}-torsion of genus two curves over 𝔽_{𝕡^{𝕞}}

Zieve, Michael

doi:10.1090/S0025-5718-10-02305-7

$p^k$-torsion of genus two curves over $\mathbb {F}_{p^m}$
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by Michael E. Zieve PDF

Math. Comp. 79 (2010), 1833-1838 Request permission

Abstract:

We determine the isogeny classes of abelian surfaces over $\mathbb {F}_q$ whose group of $\mathbb {F}_q$-rational points has order divisible by $q^2$. We also solve the same problem for Jacobians of genus-$2$ curves.

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