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PreprintCC BY 4.0arXiv

Divisibility and torsion in higher Chow groups over arithmetic fields

  • Toshiro Hiranouchi
  • Rin Sugiyama
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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 CHd+i(X,j). For a prime l different from the characteristic of F, we prove divisibility and torsion-freeness results when i≥ the l-cohomological dimension of F. If X is smooth proper and geometrically irreducible, we also study the kernel of the push-forward CHd+i(X,j)→ CHi(F,j). We apply these results to finite fields, local fields, and global fields.

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Cite

BibTeXRIS
BibTeX
@misc{hiranouchi2026divisibility,
  title = {{Divisibility and torsion in higher Chow groups over arithmetic fields}},
  author = {Toshiro Hiranouchi and Rin Sugiyama},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11178},
  eprint = {2609.11178},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11178},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Divisibility and torsion in higher Chow groups over arithmetic fields
AU  - Toshiro Hiranouchi
AU  - Rin Sugiyama
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11178
UR  - https://arxiv.org/abs/2609.11178
AB  - 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≥ 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)→ CH^i(F,j). We apply these results to finite fields, local fields, and global fields.
ER  -