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arXiv · 2407.03048

Generalized Campana points and adelic approximation on toric varieties

Boaz Moerman
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Abstract

We introduce a general framework for studying special subsets of rational points on an algebraic variety, termed $\mathcal{M}$-points. The notion of $\mathcal{M}$-points generalizes the concepts of integral points, Campana points and Darmon points. We introduce and study $M$-approximation over number fields and function fields, which is a notion that generalizes weak and strong approximation. We show that this property implies that the set of $\mathcal{M}$-points is not thin. We then give a simple characterisation of when a split toric variety satisfies $M$-approximation, generalizing work of Nakahara and Streeter. Further, we determine when the set of $\mathcal{M}$-points on a split toric variety is thin.

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Boaz Moerman. 2024-07-03. Generalized Campana points and adelic approximation on toric varieties. https://arxiv.org/abs/2407.03048

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