Descent in Buildings
Author: Holger P. Petersson, Richard M. Weiss and Bernhard Mühlherr Series: Annals of Mathematics Studies
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 f
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Summary
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 f
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.
Critic Reviews
“An impressive tour de force. ---Bertrand R”
"An impressive tour de force."--Bertrand Remy, Jahresbericht der DMV
About the Author
Bernhard Mhlherr is professor of mathematics at the University of Giessen in Germany. Holger P. Petersson is professor emeritus of mathematics at the University of Hagen in Germany. Richard M. Weiss is the William Walker Professor of Mathematics at Tufts University. He is the author of The Structure of Spherical Buildings, Quadrangular Algebras and The Structure of Affine Buildings (all Princeton) and the coauthor with Jacques Tits of Moufang Polygons.
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