{
  "abstract": "By a result of Bogomolov and Zarhin, a K3 surface $X$ over a number field $L$ has ordinary reduction at a density 1 set of primes after passing to a finite extension of $L$. In this paper, we refine this result for non-CM K3 surfaces whose transcendental Hodge structure has endomorphism field $F$ abelian over $\\mathbb{Q}$. We further assume a condition on the connected components of the $l$-adic monodromy group of $X$, and, when $F$ is totally real, a parity condition on the rank of the transcendental lattice over $F$. Under these assumptions, we prove that the set of primes of $L$ at which $X$ has $μ$-ordinary reduction has density $1$. As a corollary, the set of primes of $L$ at which $X$ has ordinary reduction has density $1/[FL:L]$. We include explicit examples of K3 surfaces satisfying these conditions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34093",
  "author_total": 2,
  "authors": [
    {
      "name": "Trung Can"
    },
    {
      "name": "Yuxin Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cej70ytner581.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34093",
  "fulltext_url": null,
  "id": "cej70ytner581",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34093",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214713840",
  "pdf_url": "https://arxiv.org/pdf/2609.34093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cej70ytner581.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Density of $μ$-ordinary Primes for K3 Surfaces",
  "title_text": "Density of μ-ordinary Primes for K3 Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cej70ytner581",
  "venue": "arXiv",
  "versions": []
}