Separated quotients of Picard schemes

Abstract

We give some necessary and sufficient conditions for the existence of N\'{e}ron models of jacobians of semistable morphisms of arbitrary relative dimension over base schemes of arbitrary dimension. To do this, we introduce a notion of alignment for semistable morphisms over any regular base scheme, and show that the jacobian of an aligned projective semistable morphism admits a separated model with the N\'{e}ron mapping property. When the Picard scheme is smooth over the base scheme along its unit section we show that the converse holds.