Descent in Buildings (AM-190) (Annals of Mathematics Studies, 190, Band 190).
Language: English
Published by Princeton University Press, 2015
- Softcover
- Used
Seller: ANTIQUARIAT Franke BRUDDENBOOKS, Lübeck, GermanyANTIQUARIAT Franke BRUDDENBOOKS
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352 S. Das Buch ist in sehr gutem, sauberen Zustand. Ecken und Kanten minimal bestossen. -----Inhalt. 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. Preface xi PART 1. MOUFANG QUADRANGLES 1 Chapter 1. Buildings 3 Chapter 2. Quadratic Forms 13 Chapter 3. Moufang Polygons 23 Chapter 4. Moufang Quadrangles 31 Chapter 5. Linked Tori, I 41 Chapter 6. Linked Tori, II 47 Chapter 7. Quadratic Forms over a Local Field 57 Chapter 8. Quadratic Forms of Type E6, E7 and E8 69 Chapter 9. Quadratic Forms of Type F4 79 PART 2. RESIDUES IN BRUHAT-TITS BUILDINGS 83 Chapter 10. Residues 85 Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 91 Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 93 Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 101 Chapter 14. Quadrangles of Type E6, E7 and E8: Summary 109 Chapter 15. Totally Wild Quadratic Forms of Type E7 115 Chapter 16. Existence 119 Chapter 17. Quadrangles of Type F4 129 Chapter 18. The Other Bruhat-Tits Buildings 137 PART 3. DESCENT 141 Chapter 19. Coxeter Groups 143 Chapter 20. Tits Indices 153 Chapter 21. Parallel Residues 165 Chapter 22. Fixed Point Buildings 181 Chapter 23. Subbuildings 195 Chapter 24. Moufang Structures 205 Chapter 25. Fixed Apartments 217 Chapter 26. The Standard Metric 221 Chapter 27. Affine Fixed Point Buildings 233 PART 4. GALOIS INVOLUTIONS 241 Chapter 28. Pseudo-Split Buildings 243 Chapter 29. Linear Automorphisms 251 Chapter 30. Strictly Semi-linear Automorphisms 259 Chapter 31. Galois Involutions 271 Chapter 32. Unramified Galois Involutions 275 PART 5. EXCEPTIONAL TITS INDICES 285 Chapter 33. Residually Pseudo-Split Buildings 287 Chapter 34. Forms of Residually Pseudo-Split Buildings 297 Chapter 35. Orthogonal Buildings 303 Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings 309 Bibliography 327 Index 333 ISBN: 9780691166919 Due to new EU packaging regulations, we are currently unable to ship to many EU countries. Shipping to Germany, the Netherlands, Ireland, Finland, and the Baltic states is possible. Deliveries to border-based parcel lockers or cross-border parcel forwarding services remain possible. Shipping to all countries outside the EU also remains possible. Sprache: Englisch Gewicht in Gramm: 517.…
Seller Inventory # 668968
- Title
- Descent in Buildings (AM-190) (Annals of Mathematics Studies, 190, Band 190).
- Author
- Muhlherr, Bernhard, Holger P. Petersson und Richard M. Weiss:
- Publisher
- Princeton University Press
- Publication year
- 2015
- Condition
- Sehr gut
- Binding
- Broschiert, Gr.-8°
- Language
- English
- ISBN 10
- 0691166919
- ISBN 13
- 9780691166919
- Edition
- Reprint.
- Item weight
- 517 grams
- Series
- Book 51 of 202: Annals of Mathematics Studies
- Seller catalogs
- Mathematik
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.
"Synopsis" may belong to another edition of this title.
About the Author
"About the title" may belong to another edition of this title.
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