Asymptotic Dynamics on Character Varieties over Finite Fields
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913703169884160 |
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| author | Thomas, Cigole |
| author_facet | Thomas, Cigole |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Dynamics on Character Varieties over Finite Fields Thomas, Cigole Algebraic Geometry 37P55, 14M35 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. |
| title | Asymptotic Dynamics on Character Varieties over Finite Fields |
| topic | Algebraic Geometry 37P55, 14M35 |
| url | https://arxiv.org/abs/2502.16009 |