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1 results

  • Forms over number fields and weak approximation

  • C. M. SKINNER
  • Journal:
    Compositio Mathematica / Volume 106 / Issue 1 / March 1997
    Published online by Cambridge University Press:
    04 December 2007, pp. 11-29
    Print publication:
    March 1997
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  • 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.