The characteristic polynomials of abelian varieties of dimensions 3 over finite fields

TL;DR

This paper characterizes the set of possible characteristic polynomials for abelian varieties of dimension 3 over finite fields, providing a comprehensive classification of their algebraic properties.

Contribution

It offers a complete description of characteristic polynomials for dimension 3 abelian varieties over finite fields, advancing understanding of their algebraic structure.

Findings

Complete classification of characteristic polynomials for dimension 3 abelian varieties.

Identification of algebraic constraints on these polynomials.

Framework for analyzing similar problems in higher dimensions.

Abstract

We describe the set of characteristic polynomials of abelian varieties of dimension 3 over finite fields.