Normes de droites sur les surfaces cubiques

Jean-Louis Colliot-Thélène; Daniel Loughran

Normes de droites sur les surfaces cubiques

Algebraic Geometry 2018-05-16 v3

Authors: Jean-Louis Colliot-Thélène , Daniel Loughran

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 $\Delta=Pic(X)$ .

Keywords

smooth cubic surfaces picard group norms of lines finite separable extensions 3-primary quotient algebraic geometry

Cite

@article{arxiv.1704.05109,
  title  = {Normes de droites sur les surfaces cubiques},
  author = {Jean-Louis Colliot-Thélène and Daniel Loughran},
  journal= {arXiv preprint arXiv:1704.05109},
  year   = {2018}
}

Comments

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)

Normes de droites sur les surfaces cubiques

Abstract

Keywords

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