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Let $A/\mathbb{F}_q$ be an abelian variety where $q=p^r$. The $p$-rank of an abelian variety is the dimension of the geometric $p$-torsion as a $\mathbb{F}_p$ vector space: $$p\operatorname{-rank}(A) = \dim_{\mathbb{F}_p}( A(\overline{\mathbb{F}}_p)[p] ).$$

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• Review status: reviewed
• Last edited by Christelle Vincent on 2016-10-29 19:22:32
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