Del i serien Annals of Mathematics Studies

Descent in Buildings

Inbunden, Engelska, 2015

AvBernhard Mühlherr,Holger P. Petersson,Richard M. Weiss

2 379 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Finns i fler format (1)

Häftad

1 089 kr

Skickas inom 5-8 vardagar

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.

Produktinformation

Utgivningsdatum2015-09-15
Mått152 x 235 x 27 mm
Vikt635 g
FormatInbunden
SpråkEngelska
SerieAnnals of Mathematics Studies
Antal sidor352
FörlagPrinceton University Press
ISBN9780691166902

Tillhör följande kategorier

Matematikens grunder inom Naturvetenskap och teknik

Bernhard Muhlherr is professor of mathematics at the University of Giessen in Germany. Holger P. Petersson is professor emeritus of mathematics at the University of Hagen in Germany. Richard M. Weiss is the William Walker Professor of Mathematics at Tufts University. He is the author of The Structure of Spherical Buildings, Quadrangular Algebras and The Structure of Affine Buildings (all Princeton) and the coauthor with Jacques Tits of Moufang Polygons.

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

Mer från samma författare

Tits Polygons

Bernhard Muhlherr, Richard M. Weiss

Häftad, 2022

1 329 kr

Mer från samma serie

Finite Dimensional Vector Spaces

Paul R. Halmos

Häftad, 1947

1 779 kr

Higher Topos Theory

Jacob Lurie

Häftad, 2009

1 269 kr

Introduction to Toric Varieties

William Fulton

Häftad, 1993

1 079 kr

Commensurabilities among Lattices in PU (1,n)

Pierre R. Deligne, George Daniel Mostow

Häftad, 1993

1 209 kr

Real Fatou Conjecture

Jacek Graczyk, Grzegorz Swiatek

Häftad, 1998

939 kr

Rigid Local Systems

Nicholas M. Katz

Häftad, 1995

1 269 kr

Renormalization and 3-Manifolds Which Fiber over the Circle

Curtis T. McMullen

Häftad, 1996

2 199 kr

Admissible Dual of GL(N) via Compact Open Subgroups

Colin J. Bushnell, Philip C. Kutzko

Häftad, 1993

1 319 kr

Global Surgery Formula for the Casson-Walker Invariant

Christine Lescop

Häftad, 1996

1 079 kr

Combinatorics of Train Tracks

Robert C. Penner, John L. Harer

Häftad, 1991

1 269 kr

Du kanske också är intresserad av