On the flatness of spin local models for split even orthogonal groups

Jie Yang

On the flatness of spin local models for split even orthogonal groups

Number Theory 2026-05-15 v2

Authors: Jie Yang

Abstract

Let $F$ be a complete discretely valued field with ring of integers $\mathcal{O}$ and residue field of characteristic $p>2$ . Let $G=\operatorname{GO}_{2n}$ denote the split orthogonal similitude group over $F$ . For any parahoric level structure, we prove that the associated spin local model for $G$ is a flat $\mathcal{O}$ -scheme with reduced special fiber. This confirms a conjecture of Pappas and Rapoport in the split case. As a corollary, we construct a flat (integral) moduli space of PEL-type D.

Keywords

algebraic stacks local-global principles group representations

Cite

@article{arxiv.2512.16704,
  title  = {On the flatness of spin local models for split even orthogonal groups},
  author = {Jie Yang},
  journal= {arXiv preprint arXiv:2512.16704},
  year   = {2026}
}

Comments

44 pp, we have removed the assumptions (i) and (ii) in Theorem 1.5 of the previous version. The manuscript now proves the flatness conjecture of Pappas--Rapoport for split orthogonal groups in full generality

On the flatness of spin local models for split even orthogonal groups

Abstract

Keywords

Cite

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