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| Main Author: | |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1910.02888 |
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| _version_ | 1866916448972046336 |
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| author | Ye, Jinhe |
| author_facet | Ye, Jinhe |
| contents | We study $μ$-stabilizers for groups definable in ACVF in the valued field sort. We prove that $\mathrm{Stab}^μ(p)$ is an infinite unbounded definable subgroup of $G$ when $p$ is standard and unbounded. In the particular case when $G$ is linear algebraic, we show that $\mathrm{Stab}^μ(p)$ is a solvable algebraic subgroup of $G$, with $\mathrm{dim}(\mathrm{Stab}^μ(p))=\mathrm{dim}(p)$ when $p$ is $μ$-reduced and unbounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_02888 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A note on $μ$-stabilizers in ACVF Ye, Jinhe Logic We study $μ$-stabilizers for groups definable in ACVF in the valued field sort. We prove that $\mathrm{Stab}^μ(p)$ is an infinite unbounded definable subgroup of $G$ when $p$ is standard and unbounded. In the particular case when $G$ is linear algebraic, we show that $\mathrm{Stab}^μ(p)$ is a solvable algebraic subgroup of $G$, with $\mathrm{dim}(\mathrm{Stab}^μ(p))=\mathrm{dim}(p)$ when $p$ is $μ$-reduced and unbounded. |
| title | A note on $μ$-stabilizers in ACVF |
| topic | Logic |
| url | https://arxiv.org/abs/1910.02888 |