# Minimal models of L*

## TL;DR

This paper classifies the minimal models of certain G_m-torsors associated with numerically trivial line bundles on abelian algebraic spaces over algebraic spaces, providing a structural understanding of these models.

## Contribution

It introduces a classification of S-minimal models of G_m-torsors derived from numerically trivial line bundles on abelian algebraic spaces, a novel structural insight.

## Key findings

- Classification of S-minimal models into two types
- Structural understanding of G_m-torsors over abelian spaces
- Framework for analyzing numerically trivial line bundles

## Abstract

Let S be an algebraic space, A an S-abelian algebraic space, L an S-fiberwise numerically trivial invertible module on A, and L* the sheaf of regular sections of L considered as a G_m-torsor on A. We classify the S-minimal models of L* into two types.