Néron models of Jacobians over bases of arbitrary dimension

Abstract

We work with a smooth relative curve $X_U/U$ with nodal reduction over an excellent and locally factorial scheme $S$. We show that blowing up a nodal model of $X_U$ in the ideal sheaf of a section yields a new nodal model, and describe how these models relate to each other. We construct a Néron model for the Jacobian of $X_U$, and describe it locally on $S$ as a quotient of the Picard space of a well-chosen nodal model. We provide a combinatorial criterion for the Néron model to be separated.

37 pages including bibliography. Comments are welcome. To appear in Épijournal de Géométrie Algébrique, Volume 6 (2022), Article No. 17

References in corpus (3)

• Geometric quadratic Chabauty
• Models of Jacobians of curves
• A monodromy criterion for existence of Neron models of abelian schemes in characteristic zero