Quotients of schemes by $\alpha_p$ or $\mu_p$ actions in characteristic p>0

TL;DR

This paper investigates the structure and local properties of schemes over fields of characteristic p>0 that admit nontrivial _p or _p actions, focusing on quotient maps and their singularities.

Contribution

It provides new theorems describing the local structure, singularities, and Picard groups of quotients by _p and _p actions in characteristic p>0.

Findings

Descriptions of local properties of quotients

Structure theorems for quotient maps

Adjunction formulas for quotients

Abstract

This paper studies schemes X defined over a field of characteristic p>0 which admit a nontrivial $\alpha_p$ or $\mu_p$ action. In particular, the structure of the quotient map $X \rightarrow Y$ is investigated. Information on local properties of the quotient Y, as singularities and local Picard groups, structure theorems for the quotient map and adjunction formulas for the quotient map are obtained.