Open problems in the wild McKay correspondence and related fields

TL;DR

This paper surveys open problems and current research directions in the wild McKay correspondence, highlighting its connections to geometry and arithmetic in positive characteristic settings.

Contribution

It compiles and discusses open problems in the wild McKay correspondence and related fields, serving as a comprehensive survey of the current state of research.

Findings

Identification of key open problems in wild McKay correspondence

Connections between wild quotient varieties and local field extensions

Summary of recent advances and challenges in the field

Abstract

The wild McKay correspondence is a form of McKay correspondence in terms of stringy invariants that is generalized to arbitrary characteristics. It gives rise to an interesting connection between the geometry of wild quotient varieties and arithmetic on extensions of local fields. The principal purpose of this article is to collect open problems on the wild McKay correspondence, as well as those in related fields that the author believes are interesting or important. It also serves as a survey on the present state of these fields.