Descent in Buildings

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

• Publisher: Princeton University Press
• Year: 2015
• Print ISBN: 9780691166919, 9780691166902
• eBook ISBN: 9781400874019
• Topic: Mathematics
• Subtopic: Algebraic Geometry
• Index: Mathematics

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their 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" Bruhat-Tits 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 Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface
• Part 1: Moufang Quadrangles
• Part 2. Residues in Bruhat-Tits Buildings
• Part 3. Descent
• Part 4. Galois Involutions
• Part 5. Exceptional Tits Indices
• Bibliography
• Index