Density of integral points in the Betti moduli of quasi-projective varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918076677619712 |
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| author | Coccia, Simone Litt, Daniel |
| author_facet | Coccia, Simone Litt, Daniel |
| contents | Let $Y$ be a smooth quasi-projective complex variety equipped with a simple normal crossings compactification. We show that integral points are potentially dense in the (relative) character varieties parametrizing $SL_2$-local systems on $Y$ with fixed algebraic integer traces along the boundary components. The proof proceeds by using work of Corlette-Simpson to reduce to the case of Riemann surfaces, where we produce an integral point with Zariski-dense orbit under the mapping class group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density of integral points in the Betti moduli of quasi-projective varieties Coccia, Simone Litt, Daniel Algebraic Geometry Geometric Topology Number Theory Let $Y$ be a smooth quasi-projective complex variety equipped with a simple normal crossings compactification. We show that integral points are potentially dense in the (relative) character varieties parametrizing $SL_2$-local systems on $Y$ with fixed algebraic integer traces along the boundary components. The proof proceeds by using work of Corlette-Simpson to reduce to the case of Riemann surfaces, where we produce an integral point with Zariski-dense orbit under the mapping class group. |
| title | Density of integral points in the Betti moduli of quasi-projective varieties |
| topic | Algebraic Geometry Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2507.00167 |