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arXiv · 1704.05109

Normes de droites sur les surfaces cubiques

Jean-Louis Colliot-Thélène·Daniel Loughran
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Abstract

Let $k$ be a field and $X \subset P^3_{k}$ 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 $\Delta=Pic(X)$.

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Jean-Louis Colliot-Thélène, Daniel Loughran. 2017-04-17. Normes de droites sur les surfaces cubiques. https://arxiv.org/abs/1704.05109

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