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arXiv · 2503.20004

Torsion higher Chow cycles modulo $\ell$

Theodosis Alexandrou·Lin Zhou
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Abstract

We study the injectivity property of certain actions of higher Chow groups on refined unramified cohomology. As an application for every $p\geq1$ and for each $d\geq p+4$ and $n\geq2,$ we establish the first examples of smooth complex projective $d$-folds $X$ such that for all $p+3\leq c\leq d-1,$ the higher Chow group $\text{CH}^{c}(X,p)$ contains infinitely many torsion cycles of order $n$ that remain linearly independent modulo $n$. Our bounds for $c$ and $d$ are also optimal. A crucial tool for the proof is morphic cohomology.

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Theodosis Alexandrou, Lin Zhou. 2025-03-25. Torsion higher Chow cycles modulo $\ell$. https://arxiv.org/abs/2503.20004

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