The Diophantine problem in isotropic reductive groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917141991653376 |
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| author | Voronetsky, Egor |
| author_facet | Voronetsky, Egor |
| contents | We begin to study model-theoretic properties of non-split isotropic reductive group schemes. In this paper we show that the base ring $K$ is e-interpretable in the point group $G(K)$ of every sufficiently isotropic reductive group scheme $G$. In particular, the Diophantine problems in $K$ and $G(K)$ are equivalent. We also compute the centralizer of the elementary subgroup of $G(K)$ and the common normalizer of all its root subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Diophantine problem in isotropic reductive groups Voronetsky, Egor Number Theory Group Theory Logic 20G99 We begin to study model-theoretic properties of non-split isotropic reductive group schemes. In this paper we show that the base ring $K$ is e-interpretable in the point group $G(K)$ of every sufficiently isotropic reductive group scheme $G$. In particular, the Diophantine problems in $K$ and $G(K)$ are equivalent. We also compute the centralizer of the elementary subgroup of $G(K)$ and the common normalizer of all its root subgroups. |
| title | The Diophantine problem in isotropic reductive groups |
| topic | Number Theory Group Theory Logic 20G99 |
| url | https://arxiv.org/abs/2504.14364 |