{
  "abstract": "Let $G$ be a finite group, $M$ a $G$-module, and $F$ a field. A continuous group homomorphism $i : Γ_L=\\text{Gal}(L_{\\text{sep}}/L) \\rightarrow G$ yields a homomorphism $i^* : H^d(G,M) \\rightarrow H^d(L,M)$ for every $d\\in \\mathbb{N}$. An element $u \\in H^d(G,M)$ is negligible over $F$ if $u\\in\\ker(i^*)$ for every $i$ and every field extension $L/F$. If $M=\\mathbb{F}_p$ for a prime $p$ with a trivial $G$-action, an element $u$ is eventually negligible over $F$ if $u^k$ is negligible over $F$ for some $k\\geq1$. The (eventually) negligible elements over $F$ form an ideal of the cohomology ring $H^*(G,\\mathbb{F}_p)$, called the (eventually) negligible ideal. We prove an analog of Quillen-Venkov for eventually negligible elements. An element $u\\in H^*(G,\\mathbb{F}_p)$ is eventually negligible over $F$ if and only if the restriction of $u$ to the cohomology of each elementary abelian $p$-subgroup of $G$ is eventually negligible over $F$. Paired with applications of a Gysin-type long exact sequence, we identify generators of the negligible ideal over $\\mathbb{Q}$ of the mod-2 cohomology of dihedral groups, cyclic $2$-groups, and generalized quaternion groups. We prove that the negligible ideal over $\\mathbb{Q}$ of the mod-2 cohomology of every finite irreducible Coxeter group is radical. The result was previously known for Weyl groups; we prove it for the remaining non-Weyl types $I_2(m)$, $H_3$, and $H_4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19251",
  "author_total": 4,
  "authors": [
    {
      "name": "Constantin Cedillo Vayson de Pradenne"
    },
    {
      "name": "Matthew Gherman"
    },
    {
      "name": "Enoch Guo"
    },
    {
      "name": "Colin La"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ad8wgd65xajr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19251",
  "fulltext_url": null,
  "id": "6ad8wgd65xajr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19251",
  "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.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221990293",
  "pdf_url": "https://arxiv.org/pdf/2610.19251",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ad8wgd65xajr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19251",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19251"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An analog of Quillen-Venkov for eventually negligible classes and radicality for finite irreducible Coxeter groups",
  "title_text": "An analog of Quillen-Venkov for eventually negligible classes and radicality for finite irreducible Coxeter groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/6ad8wgd65xajr",
  "venue": "arXiv",
  "versions": []
}