Counting the number of the twists of certain polarized abelian varieties

TL;DR

This paper counts the isomorphism classes of degree d-twists of certain polarized abelian varieties over finite fields, extending the classical elliptic curve counting problem to higher dimensions.

Contribution

It introduces a higher-dimensional analogue of the twist counting problem, providing new insights into the structure of polarized abelian varieties over finite fields.

Findings

Counts the number of isomorphism classes of degree d-twists for specific polarized abelian varieties.

Extends the classical elliptic curve twist counting problem to higher dimensions.

Provides formulas or methods for enumerating twists in the higher-dimensional setting.

Abstract

We count the number of isomorphism classes of degree $d$-twists of some polarized abelian varieties over finite fields of odd prime dimension. This can be seen as a higher dimensional analogue of the counting problem for elliptic curves case.