Quasi-compactness of N\'eron models, and an application to torsion points

TL;DR

This paper proves that Néron models of Jacobians of certain curves are quasi-compact over arbitrary bases and applies this result to analyze torsion points over number fields.

Contribution

It establishes the quasi-compactness of Néron models of Jacobians for a broad class of curves, extending their known properties to higher-dimensional bases.

Findings

Néron models are quasi-compact over arbitrary bases when they exist.

Application to torsion subgroup orders of Jacobians over number fields.

Finite type property of Néron models proven in this context.

Abstract

We prove that N\'eron models of jacobians of generically-smooth nodal curves over bases of arbitrary dimension are quasi-compact (hence of finite type) whenever they exist. We give a simple application to the orders of torsion subgroups of jacobians over number fields.