2020/07/21 by David Holmes, Samouil Molcho, Holmes, David +5 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2007.10792
openalex publication_date 2020/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the Jacobians of prestable curves over toroidal varieties always admit Néron models. These models are rarely quasi-compact or separated, but we also give a complete classification of quasi-compact separated group-models of such Jacobians. In particular we show the existence of a maximal quasi-compact separated group model, which we call the saturated model, which has the extension property for all torsion sections. The Néron model and the saturated model coincide over a Dedekind base, so the saturated model gives an alternative generalisation of the classical notion of Néron models to higher-dimensional bases; in the general case we give necessary and sufficient conditions for the Néron model and saturated model to coincide. The key result, from which most others descend, is that the logarithmic Jacobian of \citeMolcho2018The-logarithmic is a log Neron model of the Jacobian.