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arXiv · 2009.13442

On the profinite rigidity of lattices in higher rank Lie groups

Holger Kammeyer·Steffen Kionke
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Abstract

We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E_8$, $F_4$, and $G_2$. In contrast, there are arbitrarily many such examples in all other higher rank Lie groups, except possibly $\mathrm{SL}_{2n+1}(\mathbb{R})$, $\mathrm{SL}_{2n+1}(\mathbb{C})$, $\mathrm{SL}_n(\mathbb{H})$, or groups of type $E_6$.

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Holger Kammeyer, Steffen Kionke. 2020-09-28. On the profinite rigidity of lattices in higher rank Lie groups. https://arxiv.org/abs/2009.13442

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