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Droites sur les
hypersurfaces cubiques
Jean-Louis Colliot-Thélène |
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Vol. 3 (2018), No. 4, 723–728
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Abstract |
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On montre que sur toute hypersurface cubique complexe de dimension au moins 2, le groupe de Chow des cycles de dimension 1 est engendré par les droites. Le cas lisse est un théorème connu. La démonstration ici donnée repose sur un résultat sur les surfaces géométriquement rationnelles sur un corps quelconque (1983), obtenu via la K-théorie algébrique. Over any complex cubic hypersurface of dimension at least 2, the Chow group of 1-dimensional cycles is spanned by the lines lying on the hypersurface. The smooth case had already been given several other proofs. |
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Keywords
Chow groups, one-cycles, cubic hypersurfaces
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Mathematical Subject Classification 2010
Primary: 14C15, 14C25, 14C35
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Milestones
Received: 10 April 2018
Revised: 13 June 2018
Accepted: 4 July 2018
Published: 18 December 2018
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Authors |
| Jean-Louis Colliot-Thélène | |
| Laboratoire de Mathématiques
d’Orsay Université Paris-Sud, CNRS, Université Paris-Saclay 91405 Orsay France |
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