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Regular integral models of Shimura varieties and a conjecture of Pappas

  • Jie Yang
  • Ioannis Zachos
  • Zhihao Zhao
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Abstract

We construct regular integral models for a class of Shimura varieties of symplectic and orthogonal type with maximal parahoric level at an odd prime p. These models are defined over the ring of integers of the reflex field and have special fiber with normal crossings and irreducible components of multiplicity one or two. Our construction uses explicit equivariant modifications of the corresponding canonical local models for symplectic and split even orthogonal similitude groups, with the minuscule cocharacters corresponding to maximal isotropic Grassmannians. These modifications are obtained by successively blowing up Schubert varieties in the special fiber. This proves the equivariant modification conjecture of Pappas at maximal parahoric level in the above cases.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026regular,
  title = {{Regular integral models of Shimura varieties and a conjecture of Pappas}},
  author = {Jie Yang and Ioannis Zachos and Zhihao Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09475},
  eprint = {2610.09475},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09475},
}
RIS
TY  - UNPB
TI  - Regular integral models of Shimura varieties and a conjecture of Pappas
AU  - Jie Yang
AU  - Ioannis Zachos
AU  - Zhihao Zhao
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09475
UR  - https://arxiv.org/abs/2610.09475
AB  - We construct regular integral models for a class of Shimura varieties of symplectic and orthogonal type with maximal parahoric level at an odd prime p. These models are defined over the ring of integers of the reflex field and have special fiber with normal crossings and irreducible components of multiplicity one or two. Our construction uses explicit equivariant modifications of the corresponding canonical local models for symplectic and split even orthogonal similitude groups, with the minuscule cocharacters corresponding to maximal isotropic Grassmannians. These modifications are obtained by successively blowing up Schubert varieties in the special fiber. This proves the equivariant modification conjecture of Pappas at maximal parahoric level in the above cases.
ER  -