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Arithmetic purity of strong approximation for cubic hypersurfaces of large dimension
Chen Zhang
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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