Quotients of schemes by $\alpha_p$ or $\mu_p$ actions in characteristic   p>0
  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. 
Nikolaos Tziolas
math.AG