  In this paper we show that any hypersurface singularities of germs of
varieties in positive characteristic can be resolved by iterated monoidal
transformations in centers in smooth subvarieties, if we have a valuation ring
of iterated divisor type associated with the germ. Besides, we introduce
fundamental concepts for the study of resolution of singularities of germs such
as space germs, iterated analytic monoidal transformations with a normal
crossing, Weierstrass representations, reduction sequences, and so forth.

Algebraic Geometry