Equivalent computational problems for superspecial abelian surfaces

TL;DR

This paper explores the computational equivalences and reductions among key problems related to the endomorphism rings of superspecial abelian surfaces, enhancing understanding of their computational complexity.

Contribution

It establishes reductions and equivalences between problems like computing the Ibukiyama-Katsura-Oort matrix and isomorphisms of superspecial abelian surfaces.

Findings

Identifies computational equivalences between key problems.

Provides reductions that unify different computational tasks.

Enhances understanding of the complexity of endomorphism ring computations.

Abstract

We show reductions and equivalences between various problems related to the computation of the endomorphism ring of principally polarised superspecial abelian surfaces. Problems considered are the computation of the Ibukiyama-Katsura-Oort matrix and computation of unpolarised isomoprhisms between superspecial abelian surfaces.