 |
 |
|
|
| HAL: hal-00686240, version 2 |
| arXiv: 1204.1799 |
| Detailed view |  Export this paper |
 |
| Available versions: | v1 (2012-04-09) | v2 (2012-08-09) |
|
|
|
|
| Group schemes out of birational group laws, Néron models |
|
|
| Bas Edixhoven 1Matthieu Romagny 2 |
|
|
| (2012-04-08) |
|
|
|
| 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 Ariane Mézard and the second author at the Summer School "Schémas en groupes" held in the CIRM (Luminy) from 29 August to 9 September, 2011. |
|
|
|
|
|
|
|
|
|
|
|
| 1: | Mathematical institute |
|
|
|
Leiden University |
|
|
| 2: | Institut de Mathématiques de Jussieu (IMJ) |
|
|
|
CNRS : UMR7586 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
|
|
|
|
|
|
|
|
|
| Mathematisch Instituut Universiteit Leiden |
|
|
|
|
| Subject | : | Mathematics/Algebraic Geometry |
|
|
| group scheme – birational group law – Néron model |
|
|
|
| Attached file list to this document: | ||||||||||
|
||||||||||
|
|
|
| hal-00686240, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00686240 | |
| oai:hal.archives-ouvertes.fr:hal-00686240 | |
| From: Matthieu Romagny | |
| Submitted on: Thursday, 9 August 2012 17:07:04 | |
| Updated on: Thursday, 9 August 2012 21:33:35 | |
