Descent in Buildings (AM-190) / / Richard M. Weiss, Holger P. Petersson, Bernhard Mühlherr.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Mühlherr, Bernhard,; Petersson, Holger P.,; Weiss, Richard M.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2015]; ©2016
• Année de publication: 2015
• Langue: English
• Collection: Annals of Mathematics Studies ; 190
• Description matérielle: 1 online resource (352 p.) :; 22 line illus. 8 tables.
• Other title: Frontmatter --; Contents --; Preface --; PART 1. Moufang Quadrangles --; Chapter 1. Buildings --; Chapter 2. Quadratic Forms --; Chapter 3. Moufang Polygons --; Chapter 4. Moufang Quadrangles --; Chapter 5. Linked Tori, I --; Chapter 6. Linked Tori, II --; Chapter 7. Quadratic Forms over a Local Field --; Chapter 8. Quadratic Forms of Type E6, E7 and E8 --; Chapter 9. Quadratic Forms of Type F4 --; PART 2. Residues in Bruhat-Tits Buildings --; Chapter 10. Residues --; Chapter 11. Unramified Quadrangles of Type E6, E7 and E8 --; Chapter 12. Semi-ramified Quadrangles of Type E6, E7 and E8 --; Chapter 13. Ramified Quadrangles of Type E6, E7 and E8 --; Chapter 14. Quadrangles of Type E6, E7 and E8: Summary --; Chapter 15. Totally Wild Quadratic Forms of Type E7 --; Chapter 16. Existence --; Chapter 17. Quadrangles of Type F4 --; Chapter 18. The Other Bruhat-Tits Buildings --; PART 3. Descent --; Chapter 19. Coxeter Groups --; Chapter 20. Tits Indices --; Chapter 21. Parallel Residues --; Chapter 22. Fixed Point Buildings --; Chapter 23. Subbuildings --; Chapter 24. Moufang Structures --; Chapter 25. Fixed Apartments --; Chapter 26. The Standard Metric --; Chapter 27. Affine Fixed Point Buildings --; PART 4. Galois Involutions --; Chapter 28. Pseudo-Split Buildings --; Chapter 29. Linear Automorphisms --; Chapter 30. Strictly Semi-linear Automorphisms --; Chapter 31. Galois Involutions --; Chapter 32. Unramified Galois Involutions --; PART 5. Exceptional Tits Indices --; Chapter 33. Residually Pseudo-Split Buildings --; Chapter 34. Forms of Residually Pseudo-Split Buildings --; Chapter 35. Orthogonal Buildings --; Chapter 36. Indices for the Exceptional Bruhat-Tits Buildings --; Bibliography --; Index
• Résumé: 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.
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400874019; 9783110494914; 9783110665925
• DOI: 10.1515/9781400874019
• Accès: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Richard M. Weiss, Holger P. Petersson, Bernhard Mühlherr.

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 nece...