Ekedahl-Oort strata meeting the supersingular locus

@misc{muller2026ekedahloort,
  title = {{Ekedahl-Oort strata meeting the supersingular locus}},
  author = {Joseph Muller},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15024},
  eprint = {2609.15024},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15024},
}

TY  - UNPB
TI  - Ekedahl-Oort strata meeting the supersingular locus
AU  - Joseph Muller
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.15024
UR  - https://arxiv.org/abs/2609.15024
AB  - We give an explicit combinatorial criterion for an Ekedahl-Oort (EO) stratum in the moduli stack of principally polarized abelian varieties of dimension g in characteristic p > 2 to meet the supersingular locus. The criterion is obtained by translating a non-emptiness criterion for basic affine Deligne-Lusztig varieties, into an explicit condition on the elementary sequences indexing the EO strata. Furthermore, we give explicit bounds for the number of EO strata of p-rank zero which are disjoint from the supersingular locus. As a result, we prove that asymptotically almost every EO stratum of p-rank zero meets the supersingular locus. As an application, we also give a lower bound for the number of EO strata meeting the supersingular locus on unitary PEL Shimura varieties of signature (a,b).
ER  -