Moduli of finite flat torsors over nodal curves

TL;DR

This paper establishes a classification of log flat torsors over nodal curves using the log Jacobian, enabling extension of torsors from smooth fibers to the entire family under certain conditions.

Contribution

It introduces a classification framework for log flat torsors over nodal curves via the log Jacobian, connecting torsors to Cartier duals of group schemes.

Findings

Log flat torsors are classified by maps to the log Jacobian.

Fppf torsors on smooth fibers can be extended globally under regularity.

Provides a new perspective on torsor extension over nodal curves.

Abstract

We show that log flat torsors over a family $X/S$ of nodal curves under a finite flat commutative group scheme $G/S$ are classified by maps from the Cartier dual of $G$ to the log Jacobian of $X$. We deduce that fppf torsors on the smooth fibres of $X/S$ can be extended to global log flat torsors under some regularity hypotheses.