Pith Number

pith:GZ4Q5OZ7

pith:2025:GZ4Q5OZ7LLFVJC5JKUZNDOTIL5

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

Jie Yang

Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure.

arxiv:2512.16704 v2 · 2025-12-18 · math.NT

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Record completeness

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

For any parahoric level structure, the associated spin local model for G=GO_{2n} is a flat O-scheme with reduced special fiber.

C2weakest assumption

The orthogonal similitude group G is split over the complete discretely valued field F with residue characteristic p>2.

C3one 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.

References

23 extracted · 23 resolved · 0 Pith anchors

[1] G. Cliff. A basis of bideterminants for the coordinate ring of the orthogonal group . Communications in Algebra, 36(7):2719--2749, 2008 2008

[2] 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, 2013

[3] Symplectic standard tableaux 1979

[4] N. Fakhruddin, T. Haines, J. Louren c o, and T. Richarz. Singularities of local models . Mathematische Annalen, 391(4):6205--6250, 2025 2025

[5] U. G \"o rtz. On the flatness of models of certain Shimura varieties of PEL-type . Mathematische Annalen, 321(3):689--727, 2001 2001

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

On $p$-adic integral moduli schemes and local models for PEL type D

Receipt and verification

First computed	2026-05-17T23:39:00.470135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36790ebb3f5acb548ba95532d1ba685f5163a7c0be15c915dbe5f06b38c14229

Aliases

arxiv: 2512.16704 · arxiv_version: 2512.16704v2 · doi: 10.48550/arxiv.2512.16704 · pith_short_12: GZ4Q5OZ7LLFV · pith_short_16: GZ4Q5OZ7LLFVJC5J · pith_short_8: GZ4Q5OZ7

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GZ4Q5OZ7LLFVJC5JKUZNDOTIL5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 36790ebb3f5acb548ba95532d1ba685f5163a7c0be15c915dbe5f06b38c14229

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60acf13c69e87fa4835d11f1a6e1cf28f405dc619a386d287074d68e79504f41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-12-18T16:08:21Z",
    "title_canon_sha256": "51eb1052c26ea82535a94c6e9f2469adc3983c0216d75e484b2e5f7c6ba51b24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.16704",
    "kind": "arxiv",
    "version": 2
  }
}