{
  "abstract": "For a field extension $E/k$ and a Chow motive $M$, let $I_E(M)=\\ker\\bigl(\\operatorname{End}_k(M)\\longrightarrow \\operatorname{End}_E(M_E)\\bigr)$ be the base-change ideal. We establish explicit nilpotence bounds for these ideals in several geometric settings. We also prove effective generic descent: if $M$ is a summand of $h(X)(a)$ and $M_{k(X)}$ has uniform Rost exponent $s$, then $M$ has exponent $s(\\dim X+1)$. This yields the integral exponent $2n-1$ for twisted Milnor hyperplane sections of dimension $2n-2$. In characteristic zero, a weighted local-block refinement of the multilinear Rost filtration improves the uniform bounds of Gille and upgrades the elementwise estimates of Rosenschon--Sawant to uniform bounds at the ideal level. Using the Kahn--Sujatha description of pure birational motives, we obtain quantitative lifting results from birational to ordinary Chow motives, with applications to threefolds, including varieties birational to toric models and varieties admitting a decomposition of the diagonal supported on a surface. Finally, we extend the Kok--Zhou detector from individual correspondences to entire base-change ideals, obtaining an explicit ideal nilpotence bound from uniform annihilation of the critical refined unramified cohomology groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20228",
  "author_total": 1,
  "authors": [
    {
      "name": "David Kumallagov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28ejmxrcgatjy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20228",
  "fulltext_url": null,
  "id": "28ejmxrcgatjy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20228",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213577218",
  "pdf_url": "https://arxiv.org/pdf/2609.20228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28ejmxrcgatjy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Uniform Rost nilpotence and birational motives",
  "title_text": "Uniform Rost nilpotence and birational motives",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/28ejmxrcgatjy",
  "venue": "arXiv",
  "versions": []
}