Associated Schemes to the Relative Building
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Associated Schemes to the Relative Building book
This chapter explains the Root functors of the Apartment scheme, the Convex Hull scheme defined by two parabolic subgroups and the canonical affine open covering of a parabolics standard position scheme. By means of the Big Cell open covering of the Universal Schubert Cell it is proven that the Tautological Couple is in Standard Position. Thus, one obtains the finite Convex Hull scheme over the Universal Schubert Cell scheme. Recall that the Universal Schubert scheme defined by the type of relative position, is a locally trivial fibration with typical fiber, which is trivialized by the big cell open covering. The morphism is proper as is a projective scheme. As the embedding is quasi-compact and separated the schematic closure exists, satisfies, and commutes with the flat extension, where, thus there is an isomorphism.