An $l$-adic norm residue epimorphism theorem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915649321697280 |
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| author | Kahn, Bruno |
| author_facet | Kahn, Bruno |
| contents | We show that the continuous étale cohomology groups $H^n_{\mathrm{cont}}(X,\mathbf{Z}_l(n))$ of smooth varieties $X$ over a finite field $k$ are spanned as $\mathbf{Z}_l$-modules by the $n$-th Milnor $K$-sheaf locally for the Zariski topology, for all $n\ge 0$. Here $l$ is a prime invertible in $k$. This is the first general unconditional result towards the conjectures of arXiv:math/9801017 (math.AG) which put together the Tate and the Beilinson conjectures relative to algebraic cycles on smooth projective $k$-varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An $l$-adic norm residue epimorphism theorem Kahn, Bruno Algebraic Geometry Number Theory 11G25, 14C35, 19E15 We show that the continuous étale cohomology groups $H^n_{\mathrm{cont}}(X,\mathbf{Z}_l(n))$ of smooth varieties $X$ over a finite field $k$ are spanned as $\mathbf{Z}_l$-modules by the $n$-th Milnor $K$-sheaf locally for the Zariski topology, for all $n\ge 0$. Here $l$ is a prime invertible in $k$. This is the first general unconditional result towards the conjectures of arXiv:math/9801017 (math.AG) which put together the Tate and the Beilinson conjectures relative to algebraic cycles on smooth projective $k$-varieties. |
| title | An $l$-adic norm residue epimorphism theorem |
| topic | Algebraic Geometry Number Theory 11G25, 14C35, 19E15 |
| url | https://arxiv.org/abs/2409.10248 |