{
  "abstract": "In this paper, we introduce a `reduced' form of permutation twisted cohomology as introduced by Balmer--Gallauer and further developed by Miller. This ring is bigraded by a well-chosen choice of endotrivial complex, rather than multigraded by a family of endotrivial complexes. The Balmer spectrum of the small derived category of permutation modules openly immerses into the homogeneous spectrum of this ring. We also show that for $p$-groups, Miller's `remixed' twisted cohomology ring also admits the Balmer spectrum as an open subspace, and confirm in both cases it can be upgraded to have Dirac scheme structure; furthermore, we prove that the two open covers witnessing this are in general different.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40602",
  "author_total": 2,
  "authors": [
    {
      "name": "Juan Omar Gómez"
    },
    {
      "name": "Sam K. Miller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frjzad31b48n6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40602",
  "fulltext_url": null,
  "id": "frjzad31b48n6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40602",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40602",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frjzad31b48n6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40602",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40602"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Permutation twisted cohomology, reduced and immersed",
  "title_text": "Permutation twisted cohomology, reduced and immersed",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/frjzad31b48n6",
  "venue": "arXiv",
  "versions": []
}