- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
Buildings
Buildings
- Chapter:
- (p.3) Chapter One Buildings
- Source:
- Descent in Buildings (AM-190)
- Author(s):
Bernhard M¨uhlherr
Holger P. Petersson
Richard M. Weiss
- Publisher:
- Princeton University Press
This chapter assembles a few standard definitions, fixes some notation, and reviews a few of the results about buildings and Moufang polygons. It also summarizes the basic facts about Coxeter groups and buildings, including the fundamental properties of roots, residues, apartments, and projection maps. The chapter defines a Moufang building as spherical, thick, irreducible and of rank at least 2, and a Bruhat-Tits building as a thick irreducible affine building whose building at infinity is Moufang. Furthermore, it presents a fundamental result of Tits: that an irreducible thick spherical building of rank at least 3 satisfies the Moufang condition as do all the irreducible residues of rank at least 2 of such a building. Finally, it considers a simplicial complex, the dimension of which is its cardinality minus one.
Keywords: building, Moufang polygon, Coxeter group, root, residue, projection map, Moufang building, Bruhat-Tits building, spherical building, simplicial complex
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- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
