# Moderately ramified actions in positive characteristic

## TL;DR

This paper introduces a new class of wild quotient singularities in positive characteristic arising from non-linear group actions on formal power series rings, extending known classifications in characteristic two.

## Contribution

It generalizes the classification of wild Z/pZ-actions to higher dimensions and characteristics, revealing new properties of the invariant rings.

## Key findings

- Invariant rings in dimension 2 are hypersurfaces.
- In higher dimensions, invariant rings are not always complete intersections.
- Invariant rings remain quasi-Gorenstein in general.

## Abstract

In characteristic two and dimension two, wild Z/2Z-actions on k[[u,v]] ramified precisely at the origin were classified by Artin, who showed in particular that they induce hypersurface singularities. We introduce in this article a new class of wild quotient singularities in any characteristic p>0 arising from certain non-linear actions of Z/pZ on the formal power series ring in n variables. These actions are ramified precisely at the origin, and their rings of invariants in dimension n=2 are hypersurface singularities, with an equation of a form similar to the form found by Artin when p=2. In higher dimension, the rings of invariants are not local complete intersection in general, but remain quasi-Gorenstein. We establish several structure results for such actions and their corresponding rings of invariants.