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arXiv · 2606.12351

A Computational Framework for the Moduli of Supersingular Abelian Varieties

Michael Burger
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Abstract

We establish structure theorems for polarised flag type quotients arising in the study of the moduli space of supersingular abelian varieties. In particular, we prove a refined normal form for the top level of these flags and derive an explicit, computable descent criterion for quasi-polarisations. These results provide a complete classification of the first and last step of these flags. As an application, we compute polarised flag type quotients in dimensions $g\leq 5$, describing the fibers of the truncation morphisms as classification objects of supersingular abelian varieties.

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Michael Burger. 2026-06-10. A Computational Framework for the Moduli of Supersingular Abelian Varieties. https://arxiv.org/abs/2606.12351

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