Rational Points on Quartics

Abstract

Let $S\subset {\P }^n$ be a smooth quartic hypersurface defined over a number field $K$. If $n\ge 4$, then for some finite extension $K^{\prime }$ of $K$ the set $S(K^{\prime })$ of $K^{\prime }$-rational points of $S$ is Zariski dense.

32 pages; LaTeX