Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension

Chen Zhang

Source record

Source: arXiv

Published: Aug 27, 2026

arXiv: 2608.27027

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Source 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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