- 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
Residually Pseudo-Split Buildings
Residually Pseudo-Split Buildings
- Chapter:
- (p.287) Chapter Thirty Three Residually Pseudo-Split Buildings
- Source:
- Descent in Buildings (AM-190)
- Author(s):
Bernhard M¨uhlherr
Holger P. Petersson
Richard M. Weiss
- Publisher:
- Princeton University Press
This chapter presents results about a residually pseudo-split Bruhat-Tits building ΞL. It begins with a case for some quadratic space of type E⁶, E₇, and E₈ in order to identify an unramified extension such that the residue field is a pseudo-splitting field. It then considers a wild quaternion or octonion division algebra and the existence of an unramified quadratic extension L/K such that L is a splitting field of the quaternion division algebra. It also discusses the properties of an unramified extension L/K and shows that every exceptional Bruhat-Tits building is the fixed point building of a strictly semi-linear descent group of a residually pseudo-split building.
Keywords: quadratic space, Bruhat-Tits building, residue, pseudo-splitting field, octonion division algebra, unramified quadratic extension, quaternion division algebra, fixed point building, descent group, residually pseudo-split building
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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