Néron models of algebraic curves

Qing Liu (1) , Tong Jilong (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Équipe Théorie des Nombres

Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a Néron model over S, i.e., a smooth separated model of finite type satisfying the usual Néron mapping property. It is given by the smooth locus of the minimal proper regular model of X_K over S, as in the case of elliptic curves. When S is excellent, a similar result holds for connected smooth affine curves different from the affine line, with locally finite type Néron models.

Mots clés: Néron model; curve; good reduction

Domaines: Géométrie algébrique [math.AG]

Qing Liu, Tong Jilong. Néron models of algebraic curves. 2013. ⟨hal-00917694v1⟩