Group schemes out of birational group laws, Néron models

Bas Edixhoven (1) , Matthieu Romagny (2)

1 Mathematisch Instituut Universiteit Leiden
2 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: group scheme; birational group law; Néron model

Domaines: Géométrie algébrique [math.AG]

Bas Edixhoven, Matthieu Romagny. Group schemes out of birational group laws, Néron models. 2012. ⟨hal-00686240v2⟩