  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 non-perfect fields. We apply our
results to prove two conjectures due to Bosch-L\"utkebohmert-Raynaud about the
existence of N\'eron models and N\'eron 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.
