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eBook details

• Title: Descent in Buildings (AM-190)
• Author : Bernhard Mühlherr, Holger P. Petersson & Richard M. Weiss
• Release Date : January 22, 2015
• Genre: Mathematics,Books,Science & Nature,Professional & Technical,Algebra,
• Pages : * pages
• Size : 16838 KB

Description

Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-T**s 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 T**s 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-T**s building arises as a form of a "residually pseudo-split" Bruhat-T**s building. The book concludes with a display of the T**s 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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