Wild Z/pZ-actions on algebraic surfaces

An Artin-Schreier covering of the affine plane is a hypersurface in A3 defined by an equation zp−z=f(x,y). Modeling on hypersurfaces of this type, we consider in the present article a normal affine domain B with a G:=Z/pZ-action which is written in the form B=A[z], zp−sz=a with s,a∈A, where A=BG is the G-invariant subring. We also prove a classification result of Z/pZ-actions on the affine plane A2=Speck[x,y], which was first announced by S. Kuroda.