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arXiv · 2503.08925

On the computation of endomorphism rings of abelian surfaces over finite fields

Samuele Anni·Gaetan Bisson·Annamaria Iezzi·Elisa Lorenzo García·Benjamin Wesolowski
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Abstract

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each possible surface type, we survey known results and, whenever possible, provide improvements and missing results.

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Samuele Anni, Gaetan Bisson, Annamaria Iezzi, Elisa Lorenzo García, Benjamin Wesolowski. 2025-03-11. On the computation of endomorphism rings of abelian surfaces over finite fields. https://arxiv.org/abs/2503.08925

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