{
  "abstract": "We prove conductor-discriminant inequalities for all $\\mathbb{Z}/n$-covers of $\\mathbb{P}^1$ defined over discretely valued fields $K$ with excellent valuation ring $\\mathcal{O}_K$ and perfect residue field of characteristic not dividing $n$, modulo some calculations appearing in work of the third author (arXiv:2609.20585). Specifically, when such a curve $X$ is given by $y^n = f(x)$ with $f(x) \\in\\mathcal{O}_K[x]$ and $n\\mid\\text{deg}(f)$, and if $\\mathcal{X}$ is its minimal regular model over $\\mathcal{O}_K$, then the negative of the Artin conductor of $\\mathcal{X}$ is bounded above by $(n-1)v_K(\\text{disc}(\\text{rad}(f)))$. This is a direct generalization of previous work of the first two authors on hyperelliptic curves, which in turn generalized work of Ogg, Saito, Liu, and the second author. When $f$ is monic, this strengthens a result of Kohls stating that the conductor exponent of the Jacobian of such a curve is bounded above by $(n-1)v_K(\\text{disc}(\\text{rad}(f)))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20553",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew Obus"
    },
    {
      "name": "Padmavathi Srinivasan"
    },
    {
      "name": "Connor Stewart"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bzfbhx77fjzd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20553",
  "fulltext_url": null,
  "id": "6bzfbhx77fjzd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20553",
  "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": "W7213581994",
  "pdf_url": "https://arxiv.org/pdf/2609.20553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bzfbhx77fjzd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I",
  "title_text": "Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers I",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/6bzfbhx77fjzd",
  "venue": "arXiv",
  "versions": []
}