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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01212 |
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| _version_ | 1866916271369486336 |
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| author | Ren, Fei |
| author_facet | Ren, Fei |
| contents | Let $k$ be a field of positive characteristic $p$, and $X$ be a separated of finite type $k$-scheme of dimension $d$. We construct a cycle map from the additive cycle complex to the residual complex of Serre-Grothendieck coherent duality theory. This map is compatible with a cubical version of the map constructed in [Ren23] arXiv:2104.09662 when $k$ is perfect. As a corollary, we get injectivity statements for (additive) higher Chow groups as well as for motivic cohomology (with modulus) with $\mathbb{Z}/p$ coefficients when $k$ is algebraically closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additive cycle complex and coherent duality Ren, Fei Algebraic Geometry K-Theory and Homology Let $k$ be a field of positive characteristic $p$, and $X$ be a separated of finite type $k$-scheme of dimension $d$. We construct a cycle map from the additive cycle complex to the residual complex of Serre-Grothendieck coherent duality theory. This map is compatible with a cubical version of the map constructed in [Ren23] arXiv:2104.09662 when $k$ is perfect. As a corollary, we get injectivity statements for (additive) higher Chow groups as well as for motivic cohomology (with modulus) with $\mathbb{Z}/p$ coefficients when $k$ is algebraically closed. |
| title | Additive cycle complex and coherent duality |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2406.01212 |