{
  "abstract": "We study how motivic and étale motivic cohomology of a smooth and proper variety changes under extensions of algebraically closed base fields $k$. With finite coefficients, motivic cohomology is independent of $k$, and étale motivic cohomology is independent of $k$ away from the characteristic, but depends on $k$ at the characteristic. We then consider the fiber of $F-1$ for $F$ the Frobenius, on motivic cohomology and étale motivic cohomology for varieties defined over finite fields. We show that this fiber is independent of $k$ with finite coefficients. In addition, we give some results and examples with integral coefficients.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27834",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas H. Geisser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9xpp9xe6880gq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27834",
  "fulltext_url": null,
  "id": "9xpp9xe6880gq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27834",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204853747",
  "pdf_url": "https://arxiv.org/pdf/2608.27834",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9xpp9xe6880gq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2608.27834",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27834"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Frobenius rigidity for motivic cohomology",
  "title_text": "On Frobenius rigidity for motivic cohomology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/9xpp9xe6880gq",
  "venue": "arXiv",
  "versions": []
}