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PreprintarXiv licencearXiv

Profinite recognition of uniformity

  • Holger Kammeyer
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Abstract

Let G be a semisimple Lie group that is not isogenous to the isometry group of real or complex hyperbolic n-space. We show that the rational rank is a profinite invariant for irreducible lattices in G, unless G has type D2n which forms a genuine exception. In particular, profinitely isomorphic lattices in G of type D2n can have differing virtual cohomological dimension. As another corollary, uniformity is a profinite property for irreducible lattices in G outside type D4. Assuming CSP, the existence of triality symmetries gives uniform and non-uniform profinitely isomorphic lattices in type D4.

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Cite

BibTeXRIS
BibTeX
@misc{kammeyer2026profinite,
  title = {{Profinite recognition of uniformity}},
  author = {Holger Kammeyer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17041},
  eprint = {2610.17041},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17041},
}
RIS
TY  - UNPB
TI  - Profinite recognition of uniformity
AU  - Holger Kammeyer
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17041
UR  - https://arxiv.org/abs/2610.17041
AB  - Let G be a semisimple Lie group that is not isogenous to the isometry group of real or complex hyperbolic n-space. We show that the rational rank is a profinite invariant for irreducible lattices in G, unless G has type D_2n which forms a genuine exception. In particular, profinitely isomorphic lattices in G of type D_2n can have differing virtual cohomological dimension. As another corollary, uniformity is a profinite property for irreducible lattices in G outside type D_4. Assuming CSP, the existence of triality symmetries gives uniform and non-uniform profinitely isomorphic lattices in type D_4.
ER  -