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arXiv · 2609.31523

Profinite Non-Rigidity of Arithmetic Lattices and the Kähler Property

Yukun Du·Feng Hao·Kejia Zhu
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Abstract

We study the profinite non-rigidity of arithmetic lattices and its implications for the Kähler property. In the first part, we characterize the absolute Dynkin types that admit non-isomorphic real forms of higher-rank Lie groups containing torsion-free arithmetic lattices with isomorphic profinite completions. In the second part, as a geometric application, we answer a question asked independently by Arapura and Libgober, by showing that the Kählerness of finitely presented, residually finite groups is not determined by its profinite completion.

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Yukun Du, Feng Hao, Kejia Zhu. 2026-09-25. Profinite Non-Rigidity of Arithmetic Lattices and the Kähler Property. https://arxiv.org/abs/2609.31523

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