{
  "abstract": "We show that there is no maximal curve of genus five over $\\F_{64}$. As a consequence, $N_{64}(5)=140$, and the genus spectrum of maximal curves over $\\F_{64}$ is determined. The proof uses the vanishing of the third iterate of the Cartier operator. We prove that a nonhyperelliptic curve of genus five in characteristic two satisfying this condition is nontrigonal. Its canonical theta characteristic defines a separable cover of degree four with one geometric branch value. The two possible ramification types give either a rational subcanonical point or a point bound obtained from the cubic resolvent. Both cases exclude maximality over $\\F_{64}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36456",
  "author_total": 3,
  "authors": [
    {
      "name": "Gilberto B. Almeida Filho"
    },
    {
      "name": "Saeed Tafazolian"
    },
    {
      "name": "Stéfani C. Vieira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c04npyma13bvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36456",
  "fulltext_url": null,
  "id": "c04npyma13bvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36456",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214940720",
  "pdf_url": "https://arxiv.org/pdf/2609.36456",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c04npyma13bvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36456",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36456"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Nonexistence of maximal curves of genus five over $\\F_{64}$",
  "title_text": "Nonexistence of maximal curves of genus five over F_64",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/c04npyma13bvh",
  "venue": "arXiv",
  "versions": []
}