Arboreal representations of linear groups

Jorge Fariña-Asategui

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arXiv · 2506.12745

Arboreal representations of linear groups

Jorge Fariña-Asategui

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Abstract

Ab\'ert and Vir\'ag 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.

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Jorge Fariña-Asategui. 2025-06-15. Arboreal representations of linear groups. https://arxiv.org/abs/2506.12745

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