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arXiv · 2502.16009

Asymptotic Dynamics on Character Varieties over Finite Fields

Cigole Thomas
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Abstract

In this paper, we prove the lack of asymptotic transitivity of the outer automorphism group action of $\mathbb{Z}^r$ on $\mathrm{SL}_n(\mathbb{F}_q)$-character varieties of $\mathbb{Z}^r$ for $n=2,3$ and $r\geq 2$. Along the way, we stratify the character varieties and compute the $E$-polynomial, also known as the Hodge-Deligne polynomial or Serre polynomial, of these character varieties.

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Cigole Thomas. 2025-02-21. Asymptotic Dynamics on Character Varieties over Finite Fields. https://arxiv.org/abs/2502.16009

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