On Jacobians of geometrically reduced curves and their Néron models

Abstract

We study the structure of Jacobians of geometrically reduced curves over arbitrary (i.e., not necessarily perfect) fields. We show that, while such a group scheme cannot in general be decomposed into an affine and an Abelian part as over perfect fields, several important structural results for these group schemes nevertheless have close analoga over imperfect fields. We apply our results to prove two conjectures due to Bosch-Lütkebohmert-Raynaud about the existence of Néron models and Néron lft-models over excellent Dedekind schemes in the special case of Jacobians of geometrically reduced curves. Finally, we prove some existence results for semi-factorial models and related objects for general geometrically integral curves in the local case.