Descent in Buildings (AM-190)

Descent in Buildings (AM-190)

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

Print publication date: 2017

ISBN: 9780691166902

Publisher: Princeton University Press

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 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.

Table of Contents

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