{
  "abstract": "Let $X$ be a smooth scheme of dimension $d$ over a field $F$. We study the abelian-group structure of the higher Chow groups $CH^{d+i}(X,j)$. For a prime $l$ different from the characteristic of $F$, we prove divisibility and torsion-freeness results when $i\\ge$ the $l$-cohomological dimension of $F$. If $X$ is smooth proper and geometrically irreducible, we also study the kernel of the push-forward $CH^{d+i}(X,j)\\to CH^i(F,j)$. We apply these results to finite fields, local fields, and global fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11178",
  "author_total": 2,
  "authors": [
    {
      "name": "Toshiro Hiranouchi"
    },
    {
      "name": "Rin Sugiyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0h5sv8rd7p8tw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11178",
  "fulltext_url": null,
  "id": "0h5sv8rd7p8tw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11178",
  "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.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212250838",
  "pdf_url": "https://arxiv.org/pdf/2609.11178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0h5sv8rd7p8tw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Divisibility and torsion in higher Chow groups over arithmetic fields",
  "title_text": "Divisibility and torsion in higher Chow groups over arithmetic fields",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/0h5sv8rd7p8tw",
  "venue": "arXiv",
  "versions": []
}