ENGLISH

Descent in Buildings (AM-190)

By Bernhard Mühlherr; Holger P. Petersson; Richard M. Weiss

Book information

Publisher
Princeton University Press
Year
2015
ISBN
9781400874019
DOI
10.1515/9781400874019
Language
english
Format
PDF
Filesize
2 MB (1646311 bytes)
Series
Annals of Mathematics Studies; 190
Pages
352\352
Library
degruyter.com
Time added
2023-08-24 15:38:13

Description

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.

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