{
  "abstract": "Let $K$ be a Henselian discretely valued field with excellent ring of integers $\\mathcal{O}_K$ and algebraically closed residue field $k$. Let $X\\to\\mathbb{P}^1_K$ be a cyclic cover of degree $n$ prime to the characteristic of $k$. In joint work with Obus and Srinivasan (arXiv:2609.20553), we define an integer called the conductor-discriminant contribution $\\text{cdc}(y)$ associated to a multiplicity $2$ point $y$ of the branch divisor of the normalization in $K(X)$ of a regular $\\mathcal{O}_K$-model $\\mathcal{Y}$ of $\\mathbb{P}^1_{K}$; modulo several key results about $\\text{cdc}(y)$, we prove a conductor-discriminant inequality for $X$, extending previous work of Ogg, Saito, Liu, Srinivasan, and Obus$-$Srinivasan. In this companion paper, we supply the necessary technical results for $\\text{cdc}(y)$. In particular, we show $\\text{cdc}(y)$ is non-negative except under highly restrictive conditions on $n$ and the structure of the branch divisor at $y$. Moreover, if $\\text{cdc}(y)$ is negative, we show the spectrum of the complete local ring of any point lying over $y$ under the normalization of $\\mathcal{Y}$ in $K(X)$ is a rational double point. Along the way, we show the non-negativity of a related quantity, the conductor exponent-discriminant contribution $\\text{cedc}(y)$, which is used in our joint work with Obus and Srinivasan to give a new proof of a result of Kohls.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20585",
  "author_total": 1,
  "authors": [
    {
      "name": "Connor Stewart"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6vh4v9by1j6j2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20585",
  "fulltext_url": null,
  "id": "6vh4v9by1j6j2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20585",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213577048",
  "pdf_url": "https://arxiv.org/pdf/2609.20585",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6vh4v9by1j6j2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20585",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20585"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II",
  "title_text": "Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/6vh4v9by1j6j2",
  "venue": "arXiv",
  "versions": []
}