Institution: | Universität Bielefeld |
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Department: | |
Year: | 2016 |
Posted: | 02/05/2017 |
Record ID: | 2126365 |
Full text PDF: | https://pub.uni-bielefeld.de/publication/2902231 |
In 2013 Prof. Dr. Bux, Prof. Dr. Köhl and Dr. Witzel published an article on higher finiteness properties of reductive arithmetic groups in positive characteristic ([BKW13]). An essential tool in their work is the transmission of algebraic reduction theory into pure geometry: Given a semisimple linear algebraic group G and a finite product of local function fields k_f, they created a reduction theory on the building accociated to G(k_f). Later on Prof. Dr. Bux asked, whether they created the right kind of geometric reduction theory and if there is a universally valid reduction theory on arbitrary CAT(0)-spaces. As an intermediate step reaching this highly ambitious aim he asked for a second example: In this work we create an analogous reduction theory on the product of a symmetric space and a building associated to G(k_n), where k_n is a finite product of local number fields.