Author

Rin Sugiyama

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Preprint Sep 2026

Divisibility and torsion in higher Chow groups over arithmetic fields

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...

Toshiro Hiranouchi, Rin Sugiyama · 0 citations

Preprint Aug 2026

Galois Symbols for a Jacobian and Multiplicative Groups

Let $C$ be a smooth projective geometrically connected curve over a field $k$ with a $k$-rational point. Let $J$ be the Jacobian variety of $C$. For an integer $r\geq 1$ and a positive integer $n$ prime to the characteristic of $k$, we prove that the Galois symbol map \[ K(k;J,\mathbb{G}_{m},\ldots,\mathbb{G}_{m})/n \t...

Toshiro Hiranouchi, Rin Sugiyama · 0 citations