Categories of abelian varieties over finite fields I. Abelian varieties over \mathbbF_p

2015/01/11 by Tommaso Giorgio Centeleghe, Centeleghe, Tommaso Giorgio, Jakob Stix +1 · 2 citations
Computer Science · Mathematics · #11G10 #14K10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1501.02446

openalex publication_date 2015/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We assign functorially a ℤ-lattice with semisimple Frobenius action to each abelian variety over \mathbbF_p. This establishes an equivalence of categories that describes abelian varieties over \mathbbF_p avoiding √(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.

Citations

• Good Reduction of Abelian Varieties

Cited by

• An upper bound for the size of the ideal class monoid
• Isogeny graphs of abelian varieties and singular ideals in orders

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