Frobenius liftability of isolated complete intersections

We classify Frobenius liftable normal isolated complete intersection singularities of dimension at least three over an algebraically closed field of positive characteristic. In dimension three, they are precisely the regular points and the ordinary double points; in higher dimensions, they are regular. We also characterize Frobenius liftability of the complete local hypersurfaces defined by $xy-g(z,t)$ without assuming that the singularity is isolated. Such a hypersurface is Frobenius liftable if and only if, after a formal change of coordinates, $g$ is a unit times $H^p{z}^a{t}^b$ with $0\le a,b<p$.