A counterexample to the determinant approximation conjecture

@misc{kammeyer2026counterexample,
  title = {{A counterexample to the determinant approximation conjecture}},
  author = {Holger Kammeyer},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15567},
  eprint = {2609.15567},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15567},
}

TY  - UNPB
TI  - A counterexample to the determinant approximation conjecture
AU  - Holger Kammeyer
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15567
UR  - https://arxiv.org/abs/2609.15567
AB  - The determinant approximation conjecture states that for a residually finite group G and a chain G_i of finite index normal subgroups with trivial intersection, the Fuglede-Kadison determinant of every matrix over the group algebra ℚ G is the limit of the Fuglede-Kadison determinants of the matrix reductions from ℚ G to ℚ (G/G_i). We disprove the conjecture by exhibiting an explicit element of the integral group ring of the Heisenberg group with determinant equal to $2$ and reduced determinants bounded by √[3]5.
ER  -