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Descent in Buildings (AM-190) - Princeton Scholarship Online
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Descent in Buildings (AM-190)

Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss


This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or “form” of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined a ... More

Keywords: building, Bruhat-Tits building, Tits index, fixed point theory, algebraic group, subbuilding, pseudo-split building

Bibliographic Information

Print publication date: 2015 Print ISBN-13: 9780691166902
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691166902.001.0001


Affiliations are at time of print publication.

Bernhard Mühlherr, author
Universitat Giessen

Holger P. Petersson, author
FernUniversität in Hagen

Richard M. Weiss, author
Tufts University

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Part 1 Moufang Quadrangles

Part 2 Residues in Bruhat-Tits Buildings

Part 3 Descent

Part 4 Galois Involutions

Part 5 Exceptional Tits Indices

End Matter