On Jacobians of geometrically reduced curves and their N\'eron models

TL;DR

This paper investigates the structure of Jacobians of geometrically reduced curves over arbitrary fields, extending known results to non-perfect fields and proving conjectures about Néron models and related structures.

Contribution

It extends structural results of Jacobians to non-perfect fields and proves conjectures on the existence of Néron models for these Jacobians.

Findings

Structural results for Jacobians over non-perfect fields

Proof of conjectures on Néron models over Dedekind schemes

Existence results for semi-factorial models in local cases

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 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.