{
  "abstract": "Let $K$ be a number field, and let $S$ be a finite set of primes of $K$ containing all primes above $2$ and all archimedean primes. Let $G_{K,S}$ be the Galois group of the maximal algebraic extension of $K$ unramified outside $S$. We prove two refined lower bounds for the Krull dimension of unrestricted global Galois deformation rings of continuous absolutely irreducible representations of $G_{K,S}$ over finite fields of characteristic $2$. As applications, we construct the first counterexamples to the dimension conjecture in every dimension $n\\geq 2$ over every number field with a real prime. Over every totally real number field, these constructions also yield the first examples of such universal deformation rings that fail to be complete intersections. Furthermore, we propose a modified dimension conjecture for $K=\\mathbb{Q}$ and $n=2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21298",
  "author_total": 1,
  "authors": [
    {
      "name": "Yufan Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvzdc7s1q3xyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21298",
  "fulltext_url": null,
  "id": "cvzdc7s1q3xyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21298",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2610|Advanced Algebra and Geometry"
    ]
  ],
  "openalex": "W7222603074",
  "pdf_url": "https://arxiv.org/pdf/2610.21298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvzdc7s1q3xyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the dimension conjecture for global Galois deformation rings in characteristic two",
  "title_text": "On the dimension conjecture for global Galois deformation rings in characteristic two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/cvzdc7s1q3xyz",
  "venue": "arXiv",
  "versions": []
}