Prof. Dr. Petra Schwer
We prove an affine analog of Scharlau's reduction theorem for spherical buildings. To be a bit more precise let X be a euclidean building with spherical building ∂X at infinity. Then there exists a euclidean building X¯ such that X splits as a product of X¯ with some euclidean k-space such that ∂X¯ is the thick reduction of ∂X in the sense of Scharlau. \newline In addition we prove a converse statement saying that an embedding of a thick spherical building at infinity extends to an embedding of the euclidean building having the extended spherical building as its boundary.
20Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings