Pith Number

pith:ZP4DGQR6

pith:2026:ZP4DGQR6LDZPOIHO4BZAFY7PR6

not attested not anchored not stored refs pending

The Lefschetz Type Theorem For Fundamental Group Schemes

Lingguang Li, Niantao Tian

Langer positivity assumptions ensure that fundamental group schemes of ample divisors are isomorphic to those of the ambient schemes.

arxiv:2604.19546 v3 · 2026-04-21 · math.AG

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\usepackage{pith}
\pithnumber{ZP4DGQR6LDZPOIHO4BZAFY7PR6}

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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

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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

under Langer type positivity assumptions, we prove that π∗(D,x)⟶π∗(X,x) is an isomorphism for ∗∈{S,N,EN,F, EF,Loc,ELoc,ét,Eét,uni} over perfect fields.

C2weakest assumption

The Langer-type positivity assumptions on the divisor D that are invoked for the isomorphism statements.

C3one line summary

Under Langer-type positivity assumptions the fundamental group scheme of an ample divisor D is isomorphic to that of X for many variants including etale, unipotent, and local versions over perfect fields.

Receipt and verification

First computed	2026-06-10T01:11:00.511406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbf833423e58f2f720eee07202e3ef8f9c7e164bdb8dfefd039ec6233bb32d3a

Aliases

arxiv: 2604.19546 · arxiv_version: 2604.19546v3 · doi: 10.48550/arxiv.2604.19546 · pith_short_12: ZP4DGQR6LDZP · pith_short_16: ZP4DGQR6LDZPOIHO · pith_short_8: ZP4DGQR6

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/ZP4DGQR6LDZPOIHO4BZAFY7PR6 \
  | 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: cbf833423e58f2f720eee07202e3ef8f9c7e164bdb8dfefd039ec6233bb32d3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0eab478ca895bc3f5ee04ca7af8cedde93608e43991307e395865c2e63e6d061",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-21T15:04:53Z",
    "title_canon_sha256": "1a0da4460ef63f7dbb38148f27e5d27fbe63b8ac5bbb5fbda13056212bc04366"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.19546",
    "kind": "arxiv",
    "version": 3
  }
}