Descent in Buildings (AM-190), Volume I (PDF)

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Synopsis

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.

Book details

Author:
Bernhard Mühlherr, Holger P. Petersson, Richard M. Weiss
ISBN:
9781400874019
Related ISBNs:
9780691166919, 9780691166902
Publisher:
Princeton University Press
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2017-09-25
Usage restrictions:
Copyright
Copyright date:
2016
Copyright by:
Princeton University Press 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction