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

2025/12/18 by Yang, Jie
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.16704

Abstract

Let F be a complete discretely valued field with ring of integers O and residue field of characteristic p>2. Let G=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 O-scheme with reduced special fiber, provided either p is sufficiently large or n≤ 4. This partially confirms a conjecture of Pappas and Rapoport. As a corollary, we obtain a flat (integral) moduli space of PEL-type D under the same assumptions.

Citations

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Related

• Topological flatness of orthogonal spin local models
• Topological flatness of orthogonal local models in the split, even case.\n I
• Topological flatness of local models for ramified unitary groups. I. The odd dimensional case
• On the geometry of splitting models
• On the flatness of models of certain Shimura varieties of PEL-type