An explicit semi-factorial compactification of the N\'eron model

TL;DR

This paper proves that a specific semi-factorial compactification of the Néron model can be explicitly described as a moduli space of sheaves, namely the family of compactified Jacobians, using flattening techniques.

Contribution

It establishes an explicit description of the semi-factorial compactification as a moduli space of sheaves, advancing the understanding of Néron models and their compactifications.

Findings

Explicit semi-factorial compactification equals a family of compactified Jacobians.

Uses flattening technique of Raynaud--Gruson.

Connects Néron models with moduli spaces of sheaves.

Abstract

C.~P\'{e}pin recently constructed a semi-factorial compactification of the N\'{e}ron model of an abelian variety using the flattening technique of Raynaud--Gruson. Here we prove that an explicit semi-factorial compactification is a certain moduli space of sheaves --- the family of compactified jacobians.