ABSTRACT
The Universal Schubert scheme has some universal property. If the characteristics of the base scheme S are not among a fixed finite set of primes depending on the type of G, then the Schubert scheme defined by a couple, of a type of relative position and a parabolic subgroup, is obtained as the fiber of over. For the S-reductive group schemes G of a fixed type such that S satisfies the condition, it will be seen that the answers to this question and the preceding one are affirmative. From its Universal Property with respect to S-reductive group schemes of the same type the general condition on S results. The chapter discusses the Universal Schubert scheme and its smooth resolution of singularities with the corresponding objects associated with an S-reductive group scheme G of type.
