  We establish structure results for Frobenius kernels of automorphism group
schemes for surfaces of general type in positive characteristics. It turns out
that there are surprisingly few possibilities. This relies on properties of the
famous Witt algebra, which is a simple Lie algebra without finite-dimensional
counterpart over the complex numbers, together with is twisted forms. The
result actually holds true for arbitrary proper integral schemes under the
assumption that the Frobenius kernel has large isotropy group at the generic
point. This property is measured by a new numerical invariant called the
foliation rank.
