A structure theorem for euclidean buildings

Petra Schwer; David Weniger

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arXiv · 1801.10394

A structure theorem for euclidean buildings

Petra Schwer·David Weniger

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Abstract

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 $\partial X$ at infinity. Then there exists a euclidean building $\bar X$ such that $X$ splits as a product of $\bar X$ with some euclidean $k$-space such that $\partial \bar X$ is the thick reduction of $\partial X$ 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.

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Petra Schwer, David Weniger. 2018-01-31. A structure theorem for euclidean buildings. https://arxiv.org/abs/1801.10394

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