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arXiv · 1501.02446

Categories of abelian varieties over finite fields I. Abelian varieties over $\mathbb{F}_p$

Tommaso Giorgio Centeleghe·Jakob Stix
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Abstract

We assign functorially a $\mathbb{Z}$-lattice with semisimple Frobenius action to each abelian variety over $\mathbb{F}_p$. This establishes an equivalence of categories that describes abelian varieties over $\mathbb{F}_p$ avoiding $\sqrt{p}$ as an eigenvalue of Frobenius in terms of simple commutative algebra. The result extends the isomorphism classification of Waterhouse and Deligne's equivalence for ordinary abelian varieties.

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Tommaso Giorgio Centeleghe, Jakob Stix. 2015-01-11. Categories of abelian varieties over finite fields I. Abelian varieties over $\mathbb{F}_p$. https://arxiv.org/abs/1501.02446

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