{"paper":{"title":"On $p$-adic integral moduli schemes and local models for PEL type D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Spin local models for even orthogonal similitude groups are flat, normal, and Cohen-Macaulay with reduced special fibers when the residue characteristic exceeds 2.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ioannis Zachos, Jie Yang, Zhihao Zhao","submitted_at":"2026-02-27T08:53:23Z","abstract_excerpt":"We construct flat integral moduli schemes of PEL type D and the corresponding flat orthogonal Rapoport--Zink spaces with parahoric level structure over a $p$-adic integer ring. The construction relies on proving a conjecture of Pappas--Rapoport: for an even orthogonal similitude group over a complete discretely valued field of residue characteristic $p>2$, and for arbitrary parahoric level, the associated spin local model is flat, normal, Cohen--Macaulay, with reduced special fiber. In the course of the proof, we also show that in the quasi-split but non-split case, the Rapoport--Zink (naive) "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For an even orthogonal similitude group over a complete discretely valued field of residue characteristic p>2, and for arbitrary parahoric level, the associated spin local model is flat, normal, Cohen-Macaulay, with reduced special fiber.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the residue characteristic satisfies p>2, which is required to avoid characteristic-2 pathologies in the orthogonal group and its spin cover; the proof is stated only under this hypothesis.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves flatness and related properties of spin local models for PEL type D and constructs flat orthogonal Rapoport-Zink spaces with parahoric level.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spin local models for even orthogonal similitude groups are flat, normal, and Cohen-Macaulay with reduced special fibers when the residue characteristic exceeds 2.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dad478cc29617e9961e9b220cb2b07983d53289ead591b76a94a8d74a0490c33"},"source":{"id":"2602.23813","kind":"arxiv","version":2},"verdict":{"id":"283cf781-463c-4e6d-acd9-b9c9e272e645","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T19:05:28.947993Z","strongest_claim":"For an even orthogonal similitude group over a complete discretely valued field of residue characteristic p>2, and for arbitrary parahoric level, the associated spin local model is flat, normal, Cohen-Macaulay, with reduced special fiber.","one_line_summary":"Proves flatness and related properties of spin local models for PEL type D and constructs flat orthogonal Rapoport-Zink spaces with parahoric level.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the residue characteristic satisfies p>2, which is required to avoid characteristic-2 pathologies in the orthogonal group and its spin cover; the proof is stated only under this hypothesis.","pith_extraction_headline":"Spin local models for even orthogonal similitude groups are flat, normal, and Cohen-Macaulay with reduced special fibers when the residue characteristic exceeds 2."},"references":{"count":35,"sample":[{"doi":"","year":2022,"title":"J. Ansch¨ utz, I. Gleason, J. Louren¸ co, T. Richarz,On thep-adic theory of local models, to appear inAnn. of Math. (2); preprint arXiv:2201.01234 (2022)","work_id":"dd1d809c-1bb9-411a-954e-25cdf509b45d","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1990,"title":"C.-L. Chai, P. Norman,Bad reduction of the Siegel moduli scheme of genus two withΓ 0(p)- level structure,Amer. J. Math.112(1990), no. 6, 1003–1071","work_id":"e3646b91-aa17-413c-afea-3366c7764019","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1994,"title":"P. Deligne, G. Pappas,Singularit´ es des espaces de modules de Hilbert, en les caract´ eristiques divisant le discriminant,Compositio Math.90(1994), 59–79","work_id":"31bcb100-41e7-487b-933b-115ca3dd2b52","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1993,"title":"de Jong,The moduli spaces of principally polarized abelian varieties withΓ 0(p)-level struc- ture,J","work_id":"d4d3446f-f39b-4542-827d-a5f08dcc5cde","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"de Jong,Smoothness, semi-stability and alterations,Publ","work_id":"c4ba3069-3e06-4c88-816f-d5d2272bde0c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"3b7aeee111e3f5eef8f9d88b66b57f75bab3e5424753b7b6f80e1a1d80efa63c","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}