Divisibility and torsion in higher Chow groups over arithmetic fields

Toshiro Hiranouchi; Rin Sugiyama

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arXiv · 2609.11178

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 $CH^{d+i}(X,j)$. 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.

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BibTeX RIS

Toshiro Hiranouchi, Rin Sugiyama. 2026-09-10. Divisibility and torsion in higher Chow groups over arithmetic fields. https://arxiv.org/abs/2609.11178

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