Torsion higher Chow cycles modulo $\ell$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916662328950784 |
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| author | Alexandrou, Theodosis Zhou, Lin |
| author_facet | Alexandrou, Theodosis Zhou, Lin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion higher Chow cycles modulo $\ell$ Alexandrou, Theodosis Zhou, Lin Algebraic Geometry K-Theory and Homology 14C15 (primary) 14C25, 14F20 (secondary) 18F25 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. |
| title | Torsion higher Chow cycles modulo $\ell$ |
| topic | Algebraic Geometry K-Theory and Homology 14C15 (primary) 14C25, 14F20 (secondary) 18F25 |
| url | https://arxiv.org/abs/2503.20004 |