Pith Number

pith:M2SNNCSC

pith:2026:M2SNNCSCD3OZRXSUWGB4CPD4C6

not attested not anchored not stored refs pending

The Birational Invariance Of Fundamental Group Schemes

Hao Wang, Lingguang Li

Various fundamental group schemes are birationally invariant for smooth projective varieties over perfect fields.

arxiv:2604.23997 v2 · 2026-04-27 · math.AG

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\usepackage{pith}
\pithnumber{M2SNNCSCD3OZRXSUWGB4CPD4C6}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 a birational map X ⇢ Y between smooth projective varieties over a perfect field k, there exists a natural isomorphism π^*(X,x) ≅ π^*(Y,y) for any * ∈ {S,N,EN,F,EF,Loc,ELoc,ét, Eét,uni}. In particular, the induced homomorphism π^str(X,x) → π^str(Y,y) is an isomorphism for any birational morphism X → Y.

C2weakest assumption

Y is normal, the schemes are integral connected and proper over k, and the Tannakian categories C_X and C_Y satisfy the general criteria making the natural homomorphism an isomorphism; for the main application the varieties must be smooth projective over a perfect field.

C3one line summary

Various fundamental group schemes are birationally invariant for smooth projective varieties over perfect fields.

Receipt and verification

First computed	2026-06-10T01:11:00.696546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66a4d68a421edd98de54b183c13c7c178c3246f2f49688dbc95712d34b7a0328

Aliases

arxiv: 2604.23997 · arxiv_version: 2604.23997v2 · doi: 10.48550/arxiv.2604.23997 · pith_short_12: M2SNNCSCD3OZ · pith_short_16: M2SNNCSCD3OZRXSU · pith_short_8: M2SNNCSC

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/M2SNNCSCD3OZRXSUWGB4CPD4C6 \
  | 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: 66a4d68a421edd98de54b183c13c7c178c3246f2f49688dbc95712d34b7a0328

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0661c5fb480b061fbd38a7facd5deecd8384222c7427027ee0823520c4e9ee8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-27T03:23:31Z",
    "title_canon_sha256": "8114a1bcf88ffde7f45177e9722524ca95ad20c79eeb99dd94282d36ce59060b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23997",
    "kind": "arxiv",
    "version": 2
  }
}