{
  "abstract": "Let $X$ be an algebraic K3 surface defined over a global field $K$ of characteristic $0$ or $p \\geq 3$, assumed ordinary in the case where $K$ is a global function field. We provide an exact formula for the density of primes $p$ of $K$ at which the geometric Neron-Severi group of the reduction $X_p$ has a given rank in terms of the Galois representation attached to $X$. As an extension, we prove that there are infinitely many reductions of $X$ with an element of the geometric Neron-Severi group representing a fixed square class under the intersection pairing and prove results about the density of such places. In particular, we show that if $X$ corresponds to a sufficiently generic moduli point, a density zero set of places of $K$ satisfy this condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06888",
  "author_total": 1,
  "authors": [
    {
      "name": "Robin Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fhcnza15s3pc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06888",
  "fulltext_url": null,
  "id": "3fhcnza15s3pc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06888",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220915316",
  "pdf_url": "https://arxiv.org/pdf/2610.06888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fhcnza15s3pc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Densities of Picard Rank Jumps for K3 Surfaces Over Global Fields",
  "title_text": "Densities of Picard Rank Jumps for K3 Surfaces Over Global Fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/3fhcnza15s3pc",
  "venue": "arXiv",
  "versions": []
}