Arboreal representations of linear groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918059893063680 |
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| author | Fariña-Asategui, Jorge |
| author_facet | Fariña-Asategui, Jorge |
| contents | Abért and Virág conjectured in 2005 that any embedding of a linear group over a pro-$p$ domain into the group of $p$-adic automorphisms $W_p$ should be zero-dimensional. We prove their conjecture in greater generality, namely for embeddings of linear groups over any integral domain into the automorphism group of a bounded rooted tree. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arboreal representations of linear groups Fariña-Asategui, Jorge Group Theory Primary: 20E08, 28A78, 05C25, Secondary: 20F65, 20G25, 20E18 Abért and Virág conjectured in 2005 that any embedding of a linear group over a pro-$p$ domain into the group of $p$-adic automorphisms $W_p$ should be zero-dimensional. We prove their conjecture in greater generality, namely for embeddings of linear groups over any integral domain into the automorphism group of a bounded rooted tree. |
| title | Arboreal representations of linear groups |
| topic | Group Theory Primary: 20E08, 28A78, 05C25, Secondary: 20F65, 20G25, 20E18 |
| url | https://arxiv.org/abs/2506.12745 |