English

Profinite non-rigidity of arithmetic groups

Group Theory 2023-02-28 v1

Abstract

We show that for a typical high rank arithmetic lattice Γ\Gamma, there exist finite index subgroups Γ1\Gamma_{1} and Γ2\Gamma_{2} such that Γ1≄Γ2\Gamma_{1} \not\simeq \Gamma_{2} while Γ1^Γ2^\widehat{\Gamma_{1}} \simeq \widehat{\Gamma_{2}}. But there are exceptions to that rule.

Keywords

Cite

@article{arxiv.2302.13266,
  title  = {Profinite non-rigidity of arithmetic groups},
  author = {Amir Y. Weiss Behar},
  journal= {arXiv preprint arXiv:2302.13266},
  year   = {2023}
}
R2 v1 2026-06-28T08:49:45.195Z