Models of Jacobians of curves

Abstract 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 separated group-models such Jacobians. In particular, existence maximal group model, which call saturated and has extension property for all torsion sections. The model coincide Dedekind base, so gives an alternative generalization classical notion to higher-dimensional bases; in general case necessary sufficient conditions coincide. key result, from most others descend, is logarithmic Jacobian [S. Molcho J. Wise, Picard its tropicalization, preprint 2018] log Jacobian.