{"paper":{"title":"On the flatness of spin local models for split even orthogonal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jie Yang","submitted_at":"2025-12-18T16:08:21Z","abstract_excerpt":"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."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For any parahoric level structure, the associated spin local model for G=GO_{2n} is a flat O-scheme with reduced special fiber.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The orthogonal similitude group G is split over the complete discretely valued field F with residue characteristic p>2.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Spin local models for split GO_{2n} are flat O-schemes with reduced special fiber, confirming the Pappas-Rapoport conjecture in the split case.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f8e11e3bdf12a192e469a33d63f761588de59d1eb3da1bb3aa52d9af1c2fd4c9"},"source":{"id":"2512.16704","kind":"arxiv","version":2},"verdict":{"id":"326561bc-400f-4b1d-b750-a32bb2278ab8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T21:16:22.024093Z","strongest_claim":"For any parahoric level structure, the associated spin local model for G=GO_{2n} is a flat O-scheme with reduced special fiber.","one_line_summary":"Spin local models for split GO_{2n} are flat O-schemes with reduced special fiber, confirming the Pappas-Rapoport conjecture in the split case.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The orthogonal similitude group G is split over the complete discretely valued field F with residue characteristic p>2.","pith_extraction_headline":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure."},"references":{"count":23,"sample":[{"doi":"","year":2008,"title":"G. Cliff. A basis of bideterminants for the coordinate ring of the orthogonal group . Communications in Algebra, 36(7):2719--2749, 2008","work_id":"0890b03d-911b-4eac-aa48-b33c2136e16b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"S. Caracciolo, A. D. Sokal, and A. Sportiello. Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians . Advances in Applied Mathematics, 50(4):474--594,","work_id":"4f4e699e-c9bb-41b3-8ab4-7e93e2b9529c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1979,"title":"Symplectic standard tableaux","work_id":"0f24c552-fa53-46ce-b6ac-75221996b88d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"N. Fakhruddin, T. Haines, J. Louren c o, and T. Richarz. Singularities of local models . Mathematische Annalen, 391(4):6205--6250, 2025","work_id":"1fc5b602-bbbc-4894-b984-49212eec47a6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2001,"title":"U. G \\\"o rtz. On the flatness of models of certain Shimura varieties of PEL-type . Mathematische Annalen, 321(3):689--727, 2001","work_id":"3f8ea216-cb32-44f0-97d1-e9abeeb3fd88","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":23,"snapshot_sha256":"3aec78f594e727241c55a959267cc9cf63f90c2e82764bc7a479d4b841dc5d1e","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"345631b0881f8881328c1e310c186ffd1cc922bbf81bf01319a2e30e21cc39d4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}