Descent in Buildings (AM-190)

By: Bernhard Mhlherr, Holger P. Petersson, Richard M. Weiss

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Hardcover | 15 September 2015

At a Glance

Hardcover
352 Pages

Dimensions(cm)
23.4 x 15.2 x 2.54

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$380.25

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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.

Industry Reviews

"An impressive tour de force."--Bertrand Remy, Jahresbericht der DMV

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