Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Moduli of formal torsors

Fabio Tonini, Takehiko Yasuda

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.

Moduli of formal torsors

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.

Paper Structure

This paper contains 13 sections, 48 theorems, 58 equations.

Table of Contents

  1. Notation and terminology
  2. Preliminaries
  3. Some results on power series
  4. Finite and universally injective morphisms
  5. Some results on torsors
  6. Direct system of Deligne-Mumford stacks
  7. The stack of formal $G$-torsors
  8. The group $G=\mathbb{Z}/p\mathbb{Z}$ in characteristic $p$.
  9. Tame cyclic case
  10. General $p$-groups
  11. Semidirect products
  12. Limit of fibered categories
  13. Rigidification revisited

Key Result

Theorem A

Let $k$ be a field of positive characteristic $p$ and $G$ be a finite and étale group scheme over $k$ such that $G\times_{k}\overline{k}$ is a semidirect product $H\rtimes C$ of a $p$-group $H$ and a cyclic group $C$ of rank coprime with $p$.

Theorems & Definitions (115)

  • Theorem A
  • Theorem B
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Corollary 2.3
  • proof
  • Lemma 2.4
  • proof
  • ...and 105 more