Pseudo-reductive Galois descent in Bruhat-Tits buildings

• Applicant: Professor Dr. Bernhard Mühlherr
• Subject Area: Mathematics
• Term: from 2013 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 243097991

The purpose of this project is the continuation of the collaboration with Professor Richard. M. Weiss (Tufts University, Boston) on the local structure of Bruhat-Tits buildings. Observations made during his Mercaror professorship in Gießen suggest that there are interesting connections between our original question and the theory of pseudo-reductive groups. In a first step of our programme we intend to make the connection between the theory of pseudo-reductive groups and the theory of Moufang buildings more concrete. We are especially interested to find a sensible way to associate a Tits-index to a Moufang building. In a second part of our projects we intend to apply the results obtained so far in order to determine the local structure of Bruhat-Tits buildings associated to pseudo-reductive groups over fields with discrecte valuation. As a further field of application is more conceptual organisation of the proof of the classification of 2-spherical twin buildings. Finally, we want to develop a general theory for Galois descent, in order to extend the known results of Bruhat-Tits, Rousseau and others to Bruhat-Tits buildings associated with pseudo-reductive groups.

• DFG Programme: Research Grants
• International Connection: Belgium, USA
• Cooperation Partners: Professor Dr. Hendrik van Maldeghem; Dr. Koen Struyve; Professor Dr. Richard M. Weiss