  The concept of the maximal contact is the key in Hironaka's resolution
theory. It treats local theory, and it is not effective in positive
characteristics. This is the essential reason why Hironaka's theory treats only
the case of characteristic zero. In this article we propose the substitute for
the maximal contact, which is effective in any characteristics of the ground
field. We replace the maximal contact by a theorem in the theory of torus
embeddings. Using essential ideas here, we would like to establish the theory
of resolution of singularities in arbitrary characteristics in a global sense
in the forthcoming articles.
