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PreprintarXiv licencearXiv

On the asymptotic Makar-Limanov rank conjecture

  • SiZhuo Yan
  • Hao Shen
  • Jianting Yang
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Abstract

Let Bbbk be an algebraically closed field of characteristic zero and let f be a nonconstant polynomial in finitely many freely noncommuting variables. We prove the asymptotic Makar-Limanov rank conjecture, namely that the normalized rank of a value of f can be made arbitrarily small by choosing matrices over Bbbk of finite size.

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Cite

BibTeXRIS
BibTeX
@misc{yan2026asymptotic,
  title = {{On the asymptotic Makar-Limanov rank conjecture}},
  author = {SiZhuo Yan and Hao Shen and Jianting Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06800},
  eprint = {2610.06800},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06800},
}
RIS
TY  - UNPB
TI  - On the asymptotic Makar-Limanov rank conjecture
AU  - SiZhuo Yan
AU  - Hao Shen
AU  - Jianting Yang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.06800
UR  - https://arxiv.org/abs/2610.06800
AB  - Let Bbbk be an algebraically closed field of characteristic zero and let f be a nonconstant polynomial in finitely many freely noncommuting variables. We prove the asymptotic Makar-Limanov rank conjecture, namely that the normalized rank of a value of f can be made arbitrarily small by choosing matrices over Bbbk of finite size.
ER  -