Superspecial abelian varieties over finite prime fields

TL;DR

This paper counts the number of isomorphism classes of superspecial abelian varieties over finite prime fields with a specific Frobenius property, advancing understanding of their classification.

Contribution

It provides a precise enumeration of superspecial abelian varieties over prime fields with a particular Frobenius condition, a novel classification result.

Findings

Exact count of isomorphism classes of superspecial abelian varieties over _p

Characterization of Frobenius morphism _A satisfying _A^2=-p

Enhanced understanding of superspecial abelian varieties over finite fields

Abstract

In this paper we determine the number of isomorphism classes of superspecial abelian varieties $A$ over the prime field $\Fp$ such that the relative Frobenius morphism $\pi_A$ satisfying $\pi_A^2=-p$.