Néron models of algebraic curves

Qing Liu (1) , Jilong Tong (1)

1 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: good reduction; Néron model; curve

Domaines: Géométrie algébrique [math.AG]

Qing Liu, Jilong Tong. Néron models of algebraic curves. Transactions of the American Mathematical Society, 2016, 368 (10), pp.7019 - 7043. ⟨10.1090/tran/6642⟩. ⟨hal-00917694v2⟩