Geometric decomposition of abelian varieties of order 1

2021/09/09 by Toren D’Nelly-Warady, D'Nelly-Warady, Toren, Kiran S. Kedlaya +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2109.03986

openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since the 1970s, the complete classification (up to isogeny) of abelian varieties over finite fields with trivial group of rational points has been known from results of Madan--Pal and Robinson; with two exceptions these are all defined over \mathbbF₂. We determine the decomposition of these varieties into simple factors over an algebraic closure of \mathbbF₂; this requires solving a polynomial equation in three roots of unity.

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