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arXiv · 2610.06800

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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SiZhuo Yan, Hao Shen, Jianting Yang. 2026-10-06. On the asymptotic Makar-Limanov rank conjecture. https://arxiv.org/abs/2610.06800

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