Topological simplicity of the group of automorphisms of the affine plane
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912133850071040 |
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| author | Blanc, JérŔemy |
| author_facet | Blanc, JérŔemy |
| contents | We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group. In higher dimension, we show that closed normal subgroups contain all tame automorphisms.
The case of finite fields, very different, is also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological simplicity of the group of automorphisms of the affine plane Blanc, JérŔemy Algebraic Geometry 14R10, 14R20 We prove that the group $\mathrm{SAut}_{\mathrm{k}}(\mathbb{A}^2)$ is simple as an algebraic group of infinite dimension, over any infinite field $\mathrm{k}$, by proving that any closed normal subgroup is either trivial or the whole group. In higher dimension, we show that closed normal subgroups contain all tame automorphisms. The case of finite fields, very different, is also discussed. |
| title | Topological simplicity of the group of automorphisms of the affine plane |
| topic | Algebraic Geometry 14R10, 14R20 |
| url | https://arxiv.org/abs/2411.17143 |