Automorphisms and twisted forms of quotient singularities; notes on a paper of Bresciani--Vistoli

TL;DR

This paper offers a direct method for analyzing automorphisms and twisted forms of quotient singularities, extending applicability to cases with wild ramification, building on prior work involving fields of moduli and residual gerbes.

Contribution

It introduces a new direct approach to automorphisms and twisted forms that is effective even in wildly ramified scenarios, advancing the study of quotient singularities.

Findings

Provides a method that works in many wildly ramified cases

Extends previous approaches using residual gerbes

Enhances understanding of automorphisms of quotient singularities

Abstract

A recent paper of Bresciani and Vistoli studies fields of moduli using residual gerbes. One of their applications is to twisted forms of quotient singularities. We discuss a direct approach to automorphisms and twisted forms, which also works in many wildly ramified cases.