## Thibault Poiret - Néron models of Jacobians over bases of arbitrary dimension

epiga:7340 - Épijournal de Géométrie Algébrique, September 21, 2022 - https://doi.org/10.46298/epiga.2022.7340
Néron models of Jacobians over bases of arbitrary dimension

Authors: Thibault Poiret

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.

Published on: September 21, 2022
Accepted on: June 1, 2022
Submitted on: April 9, 2021
Keywords: Mathematics - Algebraic Geometry,Mathematics - Commutative Algebra,Mathematics - Number Theory