Pappas–Rapoport flatness conjecture for orthogonal spin local models

Let FF be a complete discretely valued field with ring of integers O\mathcal{O}, uniformizer π\pi, and residue field kk of characteristic p>2p>2. Let V=F2nV=F^{2n} with a split non-degenerate symmetric bilinear form, let G=GO⁡(V,ψ)G=\operatorname{GO}(V,\psi), and let L\mathcal{L} be a self-dual periodic lattice chain. The naive local model MLnaive\mathcal{M}^{\mathrm{naive}}_{\mathcal{L}} has generic fiber the orthogonal Grassmannian OGr⁡(n,2n)F\operatorname{OGr}(n,2n)_F, and the spin local model ML±\mathcal{M}^{\pm}_{\mathcal{L}} is the closed subscheme defined by the spin ±\pm-condition. Pappas–Rapoport's conjecture. The spin local model ML±\mathcal{M}^{\pm}_{\mathcal{L}} is flat over O\mathcal{O}. This conjecture proposes that the spin condition corrects the non-flatness of the naive local model for split even orthogonal similitude groups at arbitrary parahoric level. The source does not state whether the conjecture is resolved.

References

Primary source

Jie Yang, “Topological flatness of orthogonal spin local models”, arXiv:2512.16646 (2025).

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