Quotients of schemes by ${\alpha }_p$ or ${\mu }_p$ actions in characteristic p>0

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 $X\to Y$ 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.

arXiv commentRevised version. A section has been added which contains additional material about the singularities of the quotient of a normal scheme by a nontrivial ${\mu }_p$ or ${\alpha }_p$ action. 34 pages