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Normes de droites sur les surfaces cubiques
- Source :
- Colliot-Thelene, J L & Loughran, D 2018, ' Normes de droites sur les surfaces cubiques ', Pure and Applied Mathematics Quarterly, vol. 13, pp. 123-130 . https://doi.org/10.4310/pamq.2017.v13.n1.a4
- Publication Year :
- 2017
-
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 $\Delta=Pic(X)$.<br />Comment: 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)
Details
- Language :
- French
- Database :
- OpenAIRE
- Journal :
- Colliot-Thelene, J L & Loughran, D 2018, ' Normes de droites sur les surfaces cubiques ', Pure and Applied Mathematics Quarterly, vol. 13, pp. 123-130 . https://doi.org/10.4310/pamq.2017.v13.n1.a4
- Accession number :
- edsair.doi.dedup.....c401a98396ce85dc0448d4d841af4f96