  The aim of this article is the classification of simple 0-dimensional
isolated complete intersection singularities in positive characteristic. As
usual, a singularity is called simple or 0-modal if there are only finitely
many isomorphism classes of singularities into which the given singularity can
deform. The notion of simpleness was introduced by V. I. Arnold and the
classification of low modality singularities has become a fundamental task in
singularity theory. Simple complex analytic isolated complete intersection
singularities (ICIS) were classified by M. Giusti. However, the classification
in positive characteristic requires different methods and is much more
involved. The final result is nevertheless similar to the classification in
characteristic 0 with some additional normal forms in low characteristic. The
theoretical results in this paper mainly concern families of ICIS that are
formal in the fiber and algebraic in the base (formal deformation theory is not
sufficient). In particular, we give a definition of modality in this situation
and prove its semicontinuity.
