Normes de droites sur les surfaces cubiques

Abstract

Let $k$ be a field and $X\subset P_k^3$ a smooth cubic surface. Let $\Delta \subset Pic(X)$ be the finite index subgroup spanned by norms of lines on $X_K$ for $K$ running through the finite separable extensions of $k$. The quotient $Pic(X)/\Delta$ is 3-primary. If $X$ contains a line defined over $k$, then $\Delta =Pic(X)$.

8 pages, in French; now a joint paper with Daniel Loughran; this version supersedes the earlier arXiv text with the same title; to appear in Pure and Applied Mathematics Quaterly (issue in honour of Prof. Manin's 80th birthday)