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arXiv · 2608.27027

Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension

Chen Zhang
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Abstract

In this paper, we establish the arithmetic purity of strong approximation for smooth geometrically integral cubic hypersurfaces $X\subset \mathbb{P}^n$ over number fields $k$, provided that $n\ge 323$. For $k=\mathbb{Q}$, the bound can be lowered to $n \ge 30$.

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Chen Zhang. 2026-08-27. Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension. https://arxiv.org/abs/2608.27027

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