On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields

TL;DR

This paper classifies possible characteristic polynomials of Frobenius for simple supersingular abelian varieties of dimensions up to 7 over finite fields, providing a comprehensive list for odd powers of prime fields.

Contribution

It systematically determines the characteristic polynomials of Frobenius for supersingular abelian varieties of dimensions 1 to 7 over finite fields with odd exponents.

Findings

List of possible characteristic polynomials for each dimension

Complete classification for dimensions 1 to 7

Results applicable to understanding supersingular abelian varieties

Abstract

In this article, we derive a list of possible characteristic polynomials of the Frobenius of simple supersingular abelian varieties of dimension 1, 2, 3, 4, 5, 6, 7 over $\mathbb{F}_q$ where $q = p^n$, n odd.