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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{du2026profinite,
  title = {{Profinite Non-Rigidity of Arithmetic Lattices and the Kähler Property}},
  author = {Yukun Du and Feng Hao and Kejia Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31523},
  eprint = {2609.31523},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31523},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Profinite Non-Rigidity of Arithmetic Lattices and the Kähler Property
AU  - Yukun Du
AU  - Feng Hao
AU  - Kejia Zhu
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.31523
UR  - https://arxiv.org/abs/2609.31523
AB  - 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.
ER  -