Néron models of jacobians over base schemes of dimension greater than 1

Abstract

We investigate to what extent the theory of Néron models of jacobians and of abel-jacobi maps extends to relative curves over base schemes of dimension greater than 1. We give a necessary and sufficient criterion for the existence of a Néron model. We use this to show that, in general, Néron models do not exist even after making a modification or even alteration of the base. On the other hand, we show that Néron models do exist outside some codimension-2 locus.

arXiv comment47 pages, to appear in Crelle. This is a completely revised version, similar to the accepted one. The statement that the Néron model is of finite type has been removed, due to a fatal error in the proof. The result still seems to be true, but it needs a little more machinery to prove, and so will appear in a future article. Comments are still very welcome