Néron models of Jacobians over bases of arbitrary dimension

2021/03/11 by Thibault Poiret, Poiret, Thibault
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Control and Dynamics of Mobile Robots #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2103.06917

openalex publication_date 2021/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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