Sur la conjecture de Tate pour les diviseurs
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910285404569600 |
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| author | Kahn, Bruno |
| author_facet | Kahn, Bruno |
| contents | We prove that the Tate conjecture in codimension $1$ over a finitely generated field follows from the same conjecture for surfaces over its prime subfield. In positive characteristic, this is due to de Jong--Morrow over $\mathbf{F}_p$ and to Ambrosi for the reduction to $\mathbf{F}_p$. We give a different proof than Ambrosi's, which also works in characteristic $0$; over $\mathbf{Q}$, the reduction to surfaces follows from a simple argument using Lefschetz's $(1,1)$ theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_05287 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sur la conjecture de Tate pour les diviseurs Kahn, Bruno Number Theory Algebraic Geometry We prove that the Tate conjecture in codimension $1$ over a finitely generated field follows from the same conjecture for surfaces over its prime subfield. In positive characteristic, this is due to de Jong--Morrow over $\mathbf{F}_p$ and to Ambrosi for the reduction to $\mathbf{F}_p$. We give a different proof than Ambrosi's, which also works in characteristic $0$; over $\mathbf{Q}$, the reduction to surfaces follows from a simple argument using Lefschetz's $(1,1)$ theorem. |
| title | Sur la conjecture de Tate pour les diviseurs |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2205.05287 |