Pith Number

pith:3PXHZ7JW

pith:2026:3PXHZ7JW3VNJADHF2R6YTGZHNO

not attested not anchored not stored refs resolved

Solvable Automorphism Groups of Varieties

Andriy Regeta, Hanspeter Kraft, Immanuel van Santen, Serge Cantat

Solvable subgroups of automorphism groups on quasi-affine varieties are algebraic when generated by irreducible families containing the identity.

arxiv:2605.13515 v1 · 2026-05-13 · math.AG · math.GR

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\usepackage{pith}
\pithnumber{3PXHZ7JW3VNJADHF2R6YTGZHNO}

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Record completeness

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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

When X is quasi-affine, a solvable subgroup of Aut(X) that is generated by an irreducible family of automorphisms containing the identity is an algebraic subgroup. Every connected solvable subgroup of Aut(X) is contained in a Borel subgroup and its derived length is ≤ n+1. If X is quasi-affine and connected and B is a Borel of derived length n+1, then X ≅ A^n and B is conjugate to the Jonquières subgroup.

C2weakest assumption

The family generating the solvable subgroup is irreducible (in the sense of algebraic geometry, presumably Zariski-irreducible) and contains the identity; the base field is algebraically closed of characteristic zero (standard but unstated in the abstract).

C3one line summary

Solvable subgroups generated by irreducible families in Aut of quasi-affine varieties are algebraic, implying connected solvable subgroups have derived length at most n+1 and that maximal Borels on A^n are Jonquières groups.

References

87 extracted · 87 resolved · 0 Pith anchors

[1] Milne, James S. , title=. 2008 , note= 2008

[2] Grothendieck, Alexander and Raynaud, Mich. Rev\^. 2003 , bdsk-url-1 = 2003

[3] Modern Algebra, Volume 2: Groups and Algebras , series = 2025

[4] Mumford, D. and Fogarty, J. and Kirwan, F. , date-added =. Geometric invariant theory , url =. 1994 , bdsk-url-1 = 1994

[5] A conjecture of 1974 · doi:10.1215/kjm/1250523277

Receipt and verification

First computed	2026-05-18T02:44:24.464165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbee7cfd36dd5a900ce5d47d899b276baa242ad3c194322287f76ca1a34e5974

Aliases

arxiv: 2605.13515 · arxiv_version: 2605.13515v1 · doi: 10.48550/arxiv.2605.13515 · pith_short_12: 3PXHZ7JW3VNJ · pith_short_16: 3PXHZ7JW3VNJADHF · pith_short_8: 3PXHZ7JW

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/3PXHZ7JW3VNJADHF2R6YTGZHNO \
  | 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: dbee7cfd36dd5a900ce5d47d899b276baa242ad3c194322287f76ca1a34e5974

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7ce16f3ec8449b8ef0b0779dfd2d3e044506feec3ab176219f47eba7af7f588",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T13:34:34Z",
    "title_canon_sha256": "020e7317d8ce7721b648cf4d7ca3846efd0712e197fdc4943d65dbb5eb6db7dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13515",
    "kind": "arxiv",
    "version": 1
  }
}