Forms over number fields and weak approximation
| Autor: | SKINNER, C. M. |
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| Zdroj: | Compositio Mathematica; March 1997, Vol. 106 Issue: 1 p11-29, 19p |
| Abstrakt: | Let $K$ be a number field, and let $X \subseteq P^{s-1}_K$ be a smooth complete intersection defined over $K$. In this paper, weak approximation is shown to hold for $X$ provided $s$ exceeds some function of the degree and codimension of $X$. This is a corollary of a more general result about the number of integral points on certain affine varieties in homogeneously expanding regions. This general result is established via a suitable adaptation of the Hardy-Littlewood Circle Method. |
| Databáze: | Supplemental Index |
| Externí odkaz: |
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