{
  "abstract": "In this paper, we study elementary abelian $p$-covers of $P^1$ totally ramified at exactly two points and unramified elsewhere. Such covers are isomorphic to the rank-$\\ell$ Artin--Schreier curves $ X_{f, \\ell} : y^{p^\\ell} - y = f(x), $ where $f \\in \\bar{F}_p[x^{\\pm 1}]$ has a pole of order $d_1>0$ at $0$ and order $d_2>0$ at $\\infty$. After fixing $d_1$ and $d_2$, the cover $X_{f, \\ell}$ is generic if its Newton polygon is minimal as $f$ varies over all Laurent polynomials with pole orders $d_1$ and $d_2$. For $p$ sufficiently large relative to $d_1$ and $d_2$, we construct a combinatorial cost polygon $GL(d_1,d_2,p)$ and prove that its attainment is characterized by the nonvanishing of a homogeneous polynomial in the coefficients of $f$. Moreover, we prove that these conditions stabilize: there exists a Zariski-open dense subset $U$ in the coefficient space that is defined over $\\Q$ and depends only on $d_1$ and $d_2$, whereby for any $f$ whose coefficients lie in $U(\\overline{\\Q})$, the reduction is generic at every prime ideal above sufficiently large rational primes, and for every rank $\\ell$ permitted by the residue field. This result extends Zhu's result for one ramification point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02398",
  "author_total": 2,
  "authors": [
    {
      "name": "Robert Moore"
    },
    {
      "name": "Hui June Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d3mx8cxgm01s2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02398",
  "fulltext_url": null,
  "id": "d3mx8cxgm01s2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02398",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02398",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d3mx8cxgm01s2.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02398",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02398"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Global Generic Locus for Elementary Abelian p-covers of P^1 with two Ramification Points",
  "title_text": "A Global Generic Locus for Elementary Abelian p-covers of P^1 with two Ramification Points",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d3mx8cxgm01s2",
  "venue": "arXiv",
  "versions": []
}