Labeling abelian varieties over finite fields

TL;DR

This paper introduces a deterministic labeling method for isomorphism classes of abelian varieties over finite fields with commutative endomorphism algebra, including labels for polarizations in the ordinary case, aiding classification and identification.

Contribution

It presents a new deterministic process for labeling abelian varieties over finite fields, including polarizations in the ordinary case, enhancing classification tools.

Findings

Provides a practical, permanent label for abelian varieties over finite fields.

Includes polarization labels for ordinary abelian varieties.

Applicable to varieties with commutative endomorphism algebra.

Abstract

We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime field. In the ordinary case, we also provide labels for the polarizations they admit.