Descent in Buildings (AM-190)
Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss
Abstract
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
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 at the end to show that every exceptional Bruhat-Tits building arises as a form of a “residually pseudo-split” building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with The Structure of Spherical Buildings and The Structure of Affine Buildings.
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 |
Authors
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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