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PreprintarXiv licencearXiv

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≤ 5, describing the fibers of the truncation morphisms as classification objects of supersingular abelian varieties.

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Cite

BibTeXRIS
BibTeX
@misc{burger2026computational,
  title = {{A Computational Framework for the Moduli of Supersingular Abelian Varieties}},
  author = {Michael Burger},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.12351},
  eprint = {2606.12351},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.12351},
}
RIS
TY  - UNPB
TI  - A Computational Framework for the Moduli of Supersingular Abelian Varieties
AU  - Michael Burger
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2606.12351
UR  - https://arxiv.org/abs/2606.12351
AB  - 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≤ 5, describing the fibers of the truncation morphisms as classification objects of supersingular abelian varieties.
ER  -