Moduli of formal torsors

TL;DR

This paper constructs and analyzes the moduli stack of torsors over the formal punctured disk in characteristic p > 0, revealing its structure as a limit of well-behaved algebraic stacks.

Contribution

It introduces a new construction of the moduli stack of formal torsors for specific finite groups and proves its structure as a limit of separated Deligne-Mumford stacks.

Findings

The moduli stack is a limit of separated Deligne-Mumford stacks.

Transition maps between these stacks are finite and universally injective.

The construction applies to groups that are semidirect products of p-groups and tame cyclic groups.

Abstract

We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated Deligne-Mumford stacks with finite and universally injective transition maps.