Problems about torsors over regular rings (with an appendix by Yifei Zhao)

TL;DR

This paper surveys conjectures and techniques related to torsors under reductive groups over regular rings, providing an overview of current progress and open problems in the area.

Contribution

It compiles and discusses various conjectures and methods concerning torsors over regular rings, highlighting recent advances and unresolved issues.

Findings

Overview of key conjectures in the field

Survey of techniques used for progress

Identification of open problems

Abstract

We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.