Pith Number

pith:ZRN3NSXC

pith:2026:ZRN3NSXCSGA5USNPURKO7JEFNX

not attested not anchored not stored refs resolved

Semistable reductions and minimalities of invariants for group scheme actions on projective schemes

Rin Gotou, Y\^usuke Okuyama

For every point on a projective scheme under a reductive group action, the minimal invariant locus coincides with the semistable reduction translation locus.

arxiv:2604.25659 v2 · 2026-04-28 · math.AG · math.DS

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Claims

C1strongest claim

For every K-point x in X, the minimal invariant locus MinInvLoc_x and the semistable reduction translation locus SSRL_x coincide, and under a mild completeness assumption, they are non-empty.

C2weakest assumption

The mild completeness assumption on the field K (in addition to being algebraically closed, complete, non-archimedean and non-trivially valued) that is required for the non-emptiness of the loci.

C3one line summary

For reductive group scheme actions on projective schemes over complete non-archimedean fields, the minimal invariant locus coincides with the semistable reduction translation locus and is non-empty under mild completeness assumptions.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] 22, De Gruyter, Berlin, 2014 2014

[2] 296, Cambridge University Press, Cambridge, 2003 2003

[3] 35, Cambridge University Press, 1997 1997

[4] I [Springer, Berlin, 1993; MR1261420 (95m:90001)] and II [ibid.; MR1295240 (95m:90002)] 2001

[5] Alon Levy, The semistable reduction problem for the space of morphisms on P ^n , Algebra Number Theory 6(2012), no. 7, 1483--1501. 3007156 2012

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:39.509373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc5bb6cae29181da49afa454efa4856dedd618561fc0e0137f54856fb6d6ac23

Aliases

arxiv: 2604.25659 · arxiv_version: 2604.25659v2 · doi: 10.48550/arxiv.2604.25659 · pith_short_12: ZRN3NSXCSGA5 · pith_short_16: ZRN3NSXCSGA5USNP · pith_short_8: ZRN3NSXC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZRN3NSXCSGA5USNPURKO7JEFNX \
  | 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: cc5bb6cae29181da49afa454efa4856dedd618561fc0e0137f54856fb6d6ac23

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "62748d0735d2fbc3118f642cf297e1b2dc4573e94ff9871cdd966bf53f6177ec",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-28T13:57:06Z",
    "title_canon_sha256": "91aef4825e5aeca3ff90626ca4f473317bd900a47b8c926c53ac041d8673a3fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25659",
    "kind": "arxiv",
    "version": 2
  }
}