Pith Number

pith:GEQ2ZPOO

pith:2025:GEQ2ZPOOSAPSWOA27UUF5N6S2T

not attested not anchored not stored refs pending

Topics in higher ramification theory I

Franz-Viktor Kuhlmann

Nontrivial defect in an extension of degree not a prime may not imply the existence of a nonprincipal ramification ideal.

arxiv:2503.13157 v4 · 2025-03-17 · math.AC

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\pithnumber{GEQ2ZPOOSAPSWOA27UUF5N6S2T}

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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

Nontrivial defect in an extension of degree not a prime may not imply the existence of a nonprincipal ramification ideal.

C2weakest assumption

The general results on computation of ramification ideals and their connection to defect are valid in the setting of valued fields with residue characteristic p, as assumed in the standard framework of higher ramification theory.

C3one line summary

Introduces ramification ideals in higher ramification theory, computes them for Artin-Schreier and Kummer extensions of prime degree p equal to residue characteristic with or without defect, and shows an example where nontrivial defect in non-prime degree extension need not produce a nonprincipalram

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T02:04:05.417440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3121acbdce901f2b381afd285eb7d2d4e16f565b6f6f1205900a5928220b1d9c

Aliases

arxiv: 2503.13157 · arxiv_version: 2503.13157v4 · doi: 10.48550/arxiv.2503.13157 · pith_short_12: GEQ2ZPOOSAPS · pith_short_16: GEQ2ZPOOSAPSWOA2 · pith_short_8: GEQ2ZPOO

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/GEQ2ZPOOSAPSWOA27UUF5N6S2T \
  | 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: 3121acbdce901f2b381afd285eb7d2d4e16f565b6f6f1205900a5928220b1d9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb8532fa9cd6575c89761d7531a2d719ccb4575292a18abfef51592f05d78dd9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2025-03-17T13:30:33Z",
    "title_canon_sha256": "3ae061ba4535abe9b0ccb4c3f2c5905132463f06e1d600819b826b979c766960"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2503.13157",
    "kind": "arxiv",
    "version": 4
  }
}