UID:
almafu_9958352936402883
Format:
1 online resource(352 p.) :
,
illustrations.
Edition:
Electronic reproduction. Princeton, N.J. : Princeton University Press, 2015. Mode of access: World Wide Web.
Edition:
System requirements: Web browser.
Edition:
Access may be restricted to users at subscribing institutions.
ISBN:
9781400874019
Series Statement:
Annals of Mathematics Studies, 190
Content:
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.
Note:
Frontmatter --
,
Contents --
,
Preface --
,
PART 1. Moufang Quadrangles --
,
Chapter 1. Buildings --
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Chapter 2. Quadratic Forms --
,
Chapter 3. Moufang Polygons --
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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 --
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PART 2. Residues in Bruhat-Tits Buildings --
,
Chapter 10. Residues --
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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 --
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Chapter 14. Quadrangles of Type E6, E7 and E8: Summary --
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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 --
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Chapter 19. Coxeter Groups --
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Chapter 20. Tits Indices --
,
Chapter 21. Parallel Residues --
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Chapter 22. Fixed Point Buildings --
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Chapter 23. Subbuildings --
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Chapter 24. Moufang Structures --
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Chapter 25. Fixed Apartments --
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Chapter 26. The Standard Metric --
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Chapter 27. Affine Fixed Point Buildings --
,
PART 4. Galois Involutions --
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Chapter 28. Pseudo-Split Buildings --
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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
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In English.
Additional Edition:
ISBN 9780691166919
Language:
English
DOI:
10.1515/9781400874019
URL:
https://doi.org/10.1515/9781400874019
URL:
https://doi.org/10.1515/9781400874019
