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| HAL : hal-00686240, version 1 |
| arXiv : 1204.1799 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (09-04-2012) | v2 (09-08-2012) | v3 (16-06-2013) |
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| Group schemes out of birational group laws, Néron models |
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| Bas Edixhoven 1Ariane Mézard 2 |
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| (08/04/2012) |
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| In this note, we present the theorem of extension of birational group laws in both settings of classical varieties (Weil) and schemes (Artin). We improve slightly the original proof with a more direct construction of the group extension and the systematic use of algebraic spaces, and we discuss the separation properties of the group extension. We also explain the important application to the construction of Néron models of abelian varieties. This note grew out of lectures given by the second and third authors at the Summer School "Schémas en groupes" held in the CIRM (Luminy) from 29 August to 9 September, 2011. |
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| 1 : | Mathematical institute |
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Leiden University |
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| 2 : | Laboratoire de Mathématiques de Versailles (LM-Versailles) |
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CNRS : UMR8100 – Université de Versailles Saint-Quentin-en-Yvelines |
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| 3 : | Institut de Mathématiques de Jussieu (IMJ) |
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CNRS : UMR7586 – Université Pierre et Marie Curie (UPMC) - Paris VI – Université Paris VII - Paris Diderot |
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| Mathematisch Instituut Universiteit Leiden Laboratoire de Mathématiques de Versailles, UVSQ |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| group scheme – birational group law – Néron model |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00686240, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00686240 | |
| oai:hal.archives-ouvertes.fr:hal-00686240 | |
| Contributeur : Matthieu Romagny | |
| Soumis le : Dimanche 8 Avril 2012, 22:33:39 | |
| Dernière modification le : Lundi 9 Avril 2012, 07:38:26 | |
