Pith Number

pith:2Q7XFQQH

pith:2025:2Q7XFQQHJZXQACYBI2Q3WYF53N

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Height arguments toward the dynamical Mordell-Lang problem in arbitrary characteristic

Junyi Xie, She Yang

If no cohomological Lyapunov multiplier of an endomorphism iteration is an integer, then the return set of a dense orbit into a curve is finite.

arxiv:2504.01563 v4 · 2025-04-02 · math.DS · math.AG · math.NT

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Claims

C1strongest claim

For an endomorphism of a projective variety, the return set of a dense orbit into a curve is finite if any cohomological Lyapunov multiplier of any iteration is not an integer. (Abstract, result (i))

C2weakest assumption

The paper depends on the standard functoriality and Northcott-type properties of height functions continuing to hold for endomorphisms of projective varieties over fields of arbitrary characteristic, allowing the derivation of the required height inequalities from the non-integer multiplier condition. (Invoked throughout the height arguments for both (i) and (ii))

C3one line summary

Height arguments establish finiteness and structural results for return sets in the dynamical Mordell-Lang problem for endomorphisms of projective varieties and products, plus examples of complex behavior on zero-entropy tori.

Cited by

1 paper in Pith

Arithmetic Degrees are Cohomological Lyapunov Multipliers

Receipt and verification

First computed	2026-07-10T01:19:38.187622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d43f72c2074e6f000b0146a1bb60bddb7b3d9fb3c4f206a77d9ad843631b9a8c

Aliases

arxiv: 2504.01563 · arxiv_version: 2504.01563v4 · doi: 10.48550/arxiv.2504.01563 · pith_short_12: 2Q7XFQQHJZXQ · pith_short_16: 2Q7XFQQHJZXQACYB · pith_short_8: 2Q7XFQQH

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2Q7XFQQHJZXQACYBI2Q3WYF53N \
  | 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: d43f72c2074e6f000b0146a1bb60bddb7b3d9fb3c4f206a77d9ad843631b9a8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9276e626a0c153e2299db20784a6464185e49d98ec1775c1b16a62d401ab71e",
    "cross_cats_sorted": [
      "math.AG",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-04-02T10:04:14Z",
    "title_canon_sha256": "6706a534ac472d298ee21c85fab57ff23bf642935f9134c507bea6dbfac4fff1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.01563",
    "kind": "arxiv",
    "version": 4
  }
}