Étale cohomology of algebraic varieties over Stein compacta
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915619358638080 |
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| author | Benoist, Olivier |
| author_facet | Benoist, Olivier |
| contents | We prove a comparison theorem between the étale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension $n$ has cohomological dimension $n$. As an application of $\textrm{Gal}(\mathbb{C}/\mathbb{R})$-equivariant variants of these results, we obtain a quantitative version of Hilbert's 17th problem on compact subsets of real-analytic spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06054 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Étale cohomology of algebraic varieties over Stein compacta Benoist, Olivier Algebraic Geometry Complex Variables 32E10, 14F20, 11E25, 32A20, 12G10, 32C05 We prove a comparison theorem between the étale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension $n$ has cohomological dimension $n$. As an application of $\textrm{Gal}(\mathbb{C}/\mathbb{R})$-equivariant variants of these results, we obtain a quantitative version of Hilbert's 17th problem on compact subsets of real-analytic spaces. |
| title | Étale cohomology of algebraic varieties over Stein compacta |
| topic | Algebraic Geometry Complex Variables 32E10, 14F20, 11E25, 32A20, 12G10, 32C05 |
| url | https://arxiv.org/abs/2305.06054 |