Density of integral points in the Betti moduli of quasi-projective varieties

Simone Coccia; Daniel Litt

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arXiv · 2507.00167

Density of integral points in the Betti moduli of quasi-projective varieties

Simone Coccia·Daniel Litt

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Abstract

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.

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BibTeX RIS

Simone Coccia, Daniel Litt. 2025-06-30. Density of integral points in the Betti moduli of quasi-projective varieties. https://arxiv.org/abs/2507.00167

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